OEIS Similars: A172094
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A172094 | 1 1 1 3 4 1 11 17 7 1 45 76 40 10 1 197 353 216 72 13 1 903 1688 1145 458 113 16 1 4279 8257 6039 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 1 1 4 3 1 7 17 11 1 10 40 76 45 1 13 72 216 353 197 1 16 113 458 1145 1688 903 1 19 163 829 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A331969 | 1 -1 1 1 -4 1 -1 11 -7 1 1 -26 30 -10 1 -1 57 -102 58 -13 1 1 -120 303 -256 95 -16 1 -1 247 -825 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -4 1 1 -7 11 -1 1 -10 30 -26 1 1 -13 58 -102 57 -1 1 -16 95 -256 303 -120 1 1 -19 141 -515 |
| Std | Accsee docs | missing | 1 1 2 3 7 8 11 28 35 36 45 121 161 171 172 197 550 766 838 851 852 903 2591 3736 4194 4307 4323 |
| Std | AccRevsee docs | missing | 1 1 2 1 5 8 1 8 25 36 1 11 51 127 172 1 14 86 302 655 852 1 17 130 588 1733 3421 4324 1 20 183 1012 |
| Std | AntiDiagsee docs | missing | 1 1 3 1 11 4 45 17 1 197 76 7 903 353 40 1 4279 1688 216 10 20793 8257 1145 72 1 103049 41128 6039 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 3 8 3 11 34 21 4 45 152 120 40 5 197 706 648 288 65 6 903 3376 3435 1832 565 96 7 4279 16514 |
| Std | RowSum∑ k=0..n T(n, k) | A109980 | 1 2 8 36 172 852 4324 22332 116876 618084 3296308 17702412 95627580 519170004 2830862532 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A225887 | 1 1 4 18 86 426 2162 11166 58438 309042 1648154 8851206 47813790 259585002 1415431266 7747200558 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A225887 | 0 1 4 18 86 426 2162 11166 58438 309042 1648154 8851206 47813790 259585002 1415431266 7747200558 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A109980 | 1 2 8 36 172 852 4324 22332 116876 618084 3296308 17702412 95627580 519170004 2830862532 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 4 15 63 280 1297 6193 30268 150687 761487 3896016 20141649 105055521 552157572 2921461839 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 18 110 670 4054 24378 145834 868726 5157182 30529426 180307762 1062840414 6254801142 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 14 70 362 1910 10214 55154 300034 1641742 9026270 49823594 275945706 1532748918 8535244758 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 12 1309 6840 195271128 394433795280 249001897016460555 62191124612870563464 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 17 76 353 1688 8257 41128 207905 1063932 5501073 28695252 150827073 798054000 4247388417 |
| Std | ColMiddleT(n, n // 2) | missing | 1 1 4 17 40 216 458 2745 5558 35318 69660 459546 891154 6034094 11563214 79811017 151605142 |
| Std | CentralET(2 n, n) | missing | 1 4 40 458 5558 69660 891154 11563214 151605142 2003523032 26643554232 356113250388 4779679565828 |
| Std | CentralOT(2 n + 1, n) | missing | 1 17 216 2745 35318 459546 6034094 79811017 1061893830 14197476798 190591609992 2567362517418 |
| Std | ColLeftT(n, 0) | A001003 | 1 1 3 11 45 197 903 4279 20793 103049 518859 2646723 13648869 71039373 372693519 1968801519 |
| Std | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 2 12 84 630 4908 39158 317544 2605590 21571500 179838560 1507705752 12698265060 107358523496 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -4 20 -58 64 390 -2948 10934 -20320 -37440 490280 -2216764 5523504 363818 -80771124 451107110 |
| Std | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 6 34 190 1058 5890 32822 183158 1023658 5729962 32121182 180318126 1013578914 5704382226 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 14 70 362 1910 10214 55154 300034 1641742 9026270 49823594 275945706 1532748918 8535244758 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 8 54 342 2098 12634 75190 443934 2606330 15238818 88824190 516516566 2998048146 17376562314 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A331328 | 1 3 21 171 1509 13995 134277 1320651 13237221 134682219 1387100229 14430764043 151415596197 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A330802 | 1 -1 5 -33 253 -2121 18853 -174609 1667021 -16290969 162171445 -1638732129 16765758429 |
| Std | DiagRow1T(n + 1, n) | A016777 | 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 |
| Std | DiagRow2T(n + 2, n) | missing | 3 17 40 72 113 163 222 290 367 453 548 652 765 887 1018 1158 1307 1465 1632 1808 1993 2187 2390 |
| Std | DiagRow3T(n + 3, n) | missing | 11 76 216 458 829 1356 2066 2986 4143 5564 7276 9306 11681 14428 17574 21146 25171 29676 34688 |
| Std | DiagCol1T(n + 1, 1) | A239204 | 1 4 17 76 353 1688 8257 41128 207905 1063932 5501073 28695252 150827073 798054000 4247388417 |
| Std | DiagCol2T(n + 2, 2) | missing | 1 7 40 216 1145 6039 31864 168584 895209 4772655 25546224 137266704 740266449 4005875279 |
| Std | DiagCol3T(n + 3, 3) | missing | 1 10 72 458 2745 15932 90776 511548 2863593 15966390 88819632 493510966 2740862033 15222716824 |
| Std | Polysee docs | missing | 1 1 1 3 2 1 11 8 3 1 45 36 15 4 1 197 172 81 24 5 1 903 852 453 152 35 6 1 4279 4324 2583 984 255 |
| Std | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Std | PolyRow2∑ k=0..2 T(2, k) n^k | A005563 | 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728 783 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 11 36 81 152 255 396 581 816 1107 1460 1881 2376 2951 3612 4365 5216 6171 7236 8417 9720 11151 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 3 15 81 453 2583 14907 86733 507561 2982987 17588775 103976073 615916269 3654551007 21714187923 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 4 24 152 984 6440 42408 280312 1857336 12326792 81903816 544641816 3623887512 24122853096 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 15 152 1885 27612 468699 9088368 198855801 4856756660 131154927079 3883846354632 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A172094 | 1 1 -1 3 -4 1 11 -17 7 -1 45 -76 40 -10 1 197 -353 216 -72 13 -1 903 -1688 1145 -458 113 -16 1 4279 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 -1 1 1 -4 3 -1 7 -17 11 1 -10 40 -76 45 -1 13 -72 216 -353 197 1 -16 113 -458 1145 -1688 903 -1 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -7 4 1 21 -11 -7 1 369 -194 -110 10 1 -2323 1219 710 -58 -13 1 -63823 33496 19439 -1600 -321 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 4 -7 1 -7 -11 21 1 10 -110 -194 369 1 -13 -58 710 1219 -2323 1 16 -321 -1600 19439 33496 |
| Alt | Accsee docs | missing | 1 1 0 3 -1 0 11 -6 1 0 45 -31 9 -1 0 197 -156 60 -12 1 0 903 -785 360 -98 15 -1 0 4279 -3978 2061 |
| Alt | AccRevsee docs | missing | 1 -1 0 1 -3 0 -1 6 -11 0 1 -9 31 -45 0 -1 12 -60 156 -197 0 1 -15 98 -360 785 -903 0 -1 18 -145 684 |
| Alt | AntiDiagsee docs | missing | 1 1 3 -1 11 -4 45 -17 1 197 -76 7 903 -353 40 -1 4279 -1688 216 -10 20793 -8257 1145 -72 1 103049 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 1 -2 3 -8 3 11 -34 21 -4 45 -152 120 -40 5 197 -706 648 -288 65 -6 903 -3376 3435 -1832 565 -96 7 |
| Alt | RowSum∑ k=0..n T(n, k) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A225887 | 1 1 4 18 86 426 2162 11166 58438 309042 1648154 8851206 47813790 259585002 1415431266 7747200558 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A225887 | 0 -1 -4 -18 -86 -426 -2162 -11166 -58438 -309042 -1648154 -8851206 -47813790 -259585002 -1415431266 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A109980 | 1 2 8 36 172 852 4324 22332 116876 618084 3296308 17702412 95627580 519170004 2830862532 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A109980 | 1 2 8 36 172 852 4324 22332 116876 618084 3296308 17702412 95627580 519170004 2830862532 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 2 7 29 128 589 2797 13610 67515 340185 1736256 8957625 46639209 244756098 1293281695 6874880885 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A006318 | 1 1 2 6 22 90 394 1806 8558 41586 206098 1037718 5293446 27297738 142078746 745387038 3937603038 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A006318 | 1 -1 -2 -6 -22 -90 -394 -1806 -8558 -41586 -206098 -1037718 -5293446 -27297738 -142078746 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 12 1309 6840 195271128 394433795280 249001897016460555 62191124612870563464 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 17 76 353 1688 8257 41128 207905 1063932 5501073 28695252 150827073 798054000 4247388417 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 1 -4 -17 40 216 -458 -2745 5558 35318 -69660 -459546 891154 6034094 -11563214 -79811017 151605142 |
| Alt | CentralET(2 n, n) | missing | 1 -4 40 -458 5558 -69660 891154 -11563214 151605142 -2003523032 26643554232 -356113250388 |
| Alt | CentralOT(2 n + 1, n) | missing | 1 -17 216 -2745 35318 -459546 6034094 -79811017 1061893830 -14197476798 190591609992 -2567362517418 |
| Alt | ColLeftT(n, 0) | A001003 | 1 1 3 11 45 197 903 4279 20793 103049 518859 2646723 13648869 71039373 372693519 1968801519 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -4 -20 -58 -64 390 2948 10934 20320 -37440 -490280 -2216764 -5523504 363818 80771124 451107110 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 12 -84 630 -4908 39158 -317544 2605590 -21571500 179838560 -1507705752 12698265060 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A006318 | 0 -1 -2 -6 -22 -90 -394 -1806 -8558 -41586 -206098 -1037718 -5293446 -27297738 -142078746 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A006318 | 1 -1 -2 -6 -22 -90 -394 -1806 -8558 -41586 -206098 -1037718 -5293446 -27297738 -142078746 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 0 2 10 46 214 1018 4946 24470 122926 625522 3218010 16710846 87483270 461229546 2446828962 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A330802 | 1 1 5 33 253 2121 18853 174609 1667021 16290969 162171445 1638732129 16765758429 173325794409 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A331328 | 1 -3 21 -171 1509 -13995 134277 -1320651 13237221 -134682219 1387100229 -14430764043 151415596197 |
| Alt | DiagRow1T(n + 1, n) | A016777 | 1 -4 7 -10 13 -16 19 -22 25 -28 31 -34 37 -40 43 -46 49 -52 55 -58 61 -64 67 -70 73 -76 79 -82 85 |
| Alt | DiagRow2T(n + 2, n) | missing | 3 -17 40 -72 113 -163 222 -290 367 -453 548 -652 765 -887 1018 -1158 1307 -1465 1632 -1808 1993 |
| Alt | DiagRow3T(n + 3, n) | missing | 11 -76 216 -458 829 -1356 2066 -2986 4143 -5564 7276 -9306 11681 -14428 17574 -21146 25171 -29676 |
| Alt | DiagCol1T(n + 1, 1) | A239204 | -1 -4 -17 -76 -353 -1688 -8257 -41128 -207905 -1063932 -5501073 -28695252 -150827073 -798054000 |
| Alt | DiagCol2T(n + 2, 2) | missing | 1 7 40 216 1145 6039 31864 168584 895209 4772655 25546224 137266704 740266449 4005875279 |
| Alt | DiagCol3T(n + 3, 3) | missing | -1 -10 -72 -458 -2745 -15932 -90776 -511548 -2863593 -15966390 -88819632 -493510966 -2740862033 |
| Alt | Polysee docs | missing | 1 1 1 3 0 1 11 0 -1 1 45 0 -1 -2 1 197 0 -3 0 -3 1 903 0 -11 -4 3 -4 1 4279 0 -45 -12 -9 8 -5 1 |
| Alt | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 |
| Alt | PolyRow2∑ k=0..2 T(2, k) n^k | A005563 | 3 0 -1 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 11 0 -3 -4 -9 -24 -55 -108 -189 -304 -459 -660 -913 -1224 -1599 -2044 -2565 -3168 -3859 -4644 -5529 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A001003 | 1 -1 -1 -3 -11 -45 -197 -903 -4279 -20793 -103049 -518859 -2646723 -13648869 -71039373 -372693519 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 0 -4 -12 -52 -228 -1052 -5004 -24388 -121140 -611052 -3121596 -16117428 -83974212 -440941884 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -1 -4 -3 -168 1755 -36468 741881 -17546896 458552439 -13221225180 416526416757 -14242237355448 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 1 1 4 3 1 7 17 11 1 10 40 76 45 1 13 72 216 353 197 1 16 113 458 1145 1688 903 1 19 163 829 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A331969 | 1 -1 1 1 -4 1 -1 11 -7 1 1 -26 30 -10 1 -1 57 -102 58 -13 1 1 -120 303 -256 95 -16 1 -1 247 -825 |
| Rev | Accsee docs | missing | 1 1 2 1 5 8 1 8 25 36 1 11 51 127 172 1 14 86 302 655 852 1 17 130 588 1733 3421 4324 1 20 183 1012 |
| Rev | AccRevsee docs | missing | 1 1 2 3 7 8 11 28 35 36 45 121 161 171 172 197 550 766 838 851 852 903 2591 3736 4194 4307 4323 |
| Rev | AntiDiagsee docs | missing | 1 1 1 1 1 4 1 7 3 1 10 17 1 13 40 11 1 16 72 76 1 19 113 216 45 1 22 163 458 353 1 25 222 829 1145 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 8 9 1 14 51 44 1 20 120 304 225 1 26 216 864 1765 1182 1 32 339 1832 5725 10128 6321 1 38 |
| Rev | RowSum∑ k=0..n T(n, k) | A109980 | 1 2 8 36 172 852 4324 22332 116876 618084 3296308 17702412 95627580 519170004 2830862532 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A225887 | 1 1 4 18 86 426 2162 11166 58438 309042 1648154 8851206 47813790 259585002 1415431266 7747200558 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A225887 | 0 1 4 18 86 426 2162 11166 58438 309042 1648154 8851206 47813790 259585002 1415431266 7747200558 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A109980 | 1 2 8 36 172 852 4324 22332 116876 618084 3296308 17702412 95627580 519170004 2830862532 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 2 5 11 28 65 165 394 997 2419 6108 14965 37733 93038 234361 580383 1460984 3629269 9131401 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 14 70 362 1910 10214 55154 300034 1641742 9026270 49823594 275945706 1532748918 8535244758 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 18 110 670 4054 24378 145834 868726 5157182 30529426 180307762 1062840414 6254801142 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 12 1309 6840 195271128 394433795280 249001897016460555 62191124612870563464 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 17 76 353 1688 8257 41128 207905 1063932 5501073 28695252 150827073 798054000 4247388417 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 4 7 40 72 458 829 5558 10070 69660 126176 891154 1613150 11563214 20916909 151605142 274056006 |
| Rev | CentralET(2 n, n) | missing | 1 4 40 458 5558 69660 891154 11563214 151605142 2003523032 26643554232 356113250388 4779679565828 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 7 72 829 10070 126176 1613150 20916909 274056006 3619503354 48106284072 642654624970 |
| Rev | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev | ColRightT(n, n) | A001003 | 1 1 3 11 45 197 903 4279 20793 103049 518859 2646723 13648869 71039373 372693519 1968801519 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 2 12 84 630 4908 39158 317544 2605590 21571500 179838560 1507705752 12698265060 107358523496 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -4 -20 -58 -64 390 2948 10934 20320 -37440 -490280 -2216764 -5523504 363818 80771124 451107110 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 10 74 498 3202 20054 123502 751850 4539098 27233118 162605350 967212834 5735631138 33927693222 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 18 110 670 4054 24378 145834 868726 5157182 30529426 180307762 1062840414 6254801142 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 16 174 1574 12818 97618 709950 4993470 34245290 230270378 1524150038 9959253062 64384727058 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 3 15 81 453 2583 14907 86733 507561 2982987 17588775 103976073 615916269 3654551007 21714187923 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A001003 | 1 -1 -1 -3 -11 -45 -197 -903 -4279 -20793 -103049 -518859 -2646723 -13648869 -71039373 -372693519 |
| Rev | DiagRow1T(n + 1, n) | A239204 | 1 4 17 76 353 1688 8257 41128 207905 1063932 5501073 28695252 150827073 798054000 4247388417 |
| Rev | DiagRow2T(n + 2, n) | missing | 1 7 40 216 1145 6039 31864 168584 895209 4772655 25546224 137266704 740266449 4005875279 |
| Rev | DiagRow3T(n + 3, n) | missing | 1 10 72 458 2745 15932 90776 511548 2863593 15966390 88819632 493510966 2740862033 15222716824 |
| Rev | DiagCol1T(n + 1, 1) | A016777 | 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 |
| Rev | DiagCol2T(n + 2, 2) | missing | 3 17 40 72 113 163 222 290 367 453 548 652 765 887 1018 1158 1307 1465 1632 1808 1993 2187 2390 |
| Rev | DiagCol3T(n + 3, 3) | missing | 11 76 216 458 829 1356 2066 2986 4143 5564 7276 9306 11681 14428 17574 21146 25171 29676 34688 |
| Rev | Polysee docs | missing | 1 1 1 1 2 1 1 8 3 1 1 36 21 4 1 1 172 171 40 5 1 1 852 1509 472 65 6 1 1 4324 13995 6088 1005 96 7 |
| Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A000567 | 1 8 21 40 65 96 133 176 225 280 341 408 481 560 645 736 833 936 1045 1160 1281 1408 1541 1680 1825 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 36 171 472 1005 1836 3031 4656 6777 9460 12771 16776 21541 27132 33615 41056 49521 59076 69787 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A331328 | 1 3 21 171 1509 13995 134277 1320651 13237221 134682219 1387100229 14430764043 151415596197 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 4 40 472 6088 82984 1174648 17091256 253959016 3836703496 58748174680 909634368856 14217145385224 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 21 472 17065 865116 56843269 4603748976 443998810161 49729649726260 6347382387502981 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A331969 | 1 -1 1 1 -4 1 -1 11 -7 1 1 -26 30 -10 1 -1 57 -102 58 -13 1 1 -120 303 -256 95 -16 1 -1 247 -825 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -4 1 1 -7 11 -1 1 -10 30 -26 1 1 -13 58 -102 57 -1 1 -16 95 -256 303 -120 1 1 -19 141 -515 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 1 1 4 3 1 7 17 11 1 10 40 76 45 1 13 72 216 353 197 1 16 113 458 1145 1688 903 1 19 163 829 |
| Inv | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 -1 1 -5 4 1 47 -37 -11 1 1361 -1072 -316 26 1 -72507 57111 16832 -1380 -57 1 -9100733 7168300 |
| Inv | Accsee docs | missing | 1 -1 0 1 -3 -2 -1 10 3 4 1 -25 5 -5 -4 -1 56 -46 12 -1 0 1 -119 184 -72 23 7 8 -1 246 -579 376 -139 |
| Inv | AccRevsee docs | missing | 1 1 0 1 -3 -2 1 -6 5 4 1 -9 21 -5 -4 1 -12 46 -56 1 0 1 -15 80 -176 127 7 8 1 -18 123 -392 563 -262 |
| Inv | AntiDiagsee docs | A121463 | 1 -1 1 1 -1 -4 1 11 1 -1 -26 -7 1 57 30 1 -1 -120 -102 -10 1 247 303 58 1 -1 -502 -825 -256 -13 1 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 1 -8 3 -1 22 -21 4 1 -52 90 -40 5 -1 114 -306 232 -65 6 1 -240 909 -1024 475 -96 7 -1 494 |
| Inv | RowSum∑ k=0..n T(n, k) | A146559 | 1 0 -2 4 -4 0 8 -16 16 0 -32 64 -64 0 128 -256 256 0 -512 1024 -1024 0 2048 -4096 4096 0 -8192 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 -1 2 -8 32 -116 400 -1360 4624 -15760 53792 -183680 627200 -2141504 7311616 -24963328 85229824 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -4 12 -36 116 -392 1344 -4608 15760 -53824 183744 -627264 2141504 -7311488 24963072 -85229568 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A006012 | 1 -2 6 -20 68 -232 792 -2704 9232 -31520 107616 -367424 1254464 -4283008 14623104 -49926400 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A006012 | 1 2 6 20 68 232 792 2704 9232 31520 107616 367424 1254464 4283008 14623104 49926400 170459392 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A001519 | 1 -1 2 -5 13 -34 89 -233 610 -1597 4181 -10946 28657 -75025 196418 -514229 1346269 -3524578 9227465 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -4 16 -28 20 32 -128 208 -144 -192 768 -1216 832 1024 -4096 6400 -4352 -5120 20480 -31744 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -4 4 4 -20 32 -16 -48 144 -192 64 320 -832 1024 -256 -1792 4352 -5120 1024 9216 -21504 24576 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 4 77 390 730626 7368960 188416682025 147187935422220 9210398405098800 867366479041609225319424 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A297382 | 1 1 4 1 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 11 30 102 303 955 3178 9740 32354 106970 333295 1136799 3748104 11877537 40877760 134581692 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -4 11 30 -102 -256 955 2310 -9078 -21504 87374 204204 -849180 -1966080 8316627 19122246 |
| Inv | CentralET(2 n, n) | A091527 | 1 -4 30 -256 2310 -21504 204204 -1966080 19122246 -187432960 1848483780 -18320719872 182327718300 |
| Inv | CentralOT(2 n + 1, n) | missing | -1 11 -102 955 -9078 87374 -849180 8316627 -81953190 811645978 -8071975860 80560204894 |
| Inv | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -6 12 38 -220 36 2632 -6458 -18924 127724 -48136 -1580836 4343976 11041416 -84673648 49912902 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 10 56 326 1952 11908 73600 459334 2888192 18268460 116111360 740945180 4744192000 30464171720 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 -2 0 8 -20 24 0 -64 144 -160 0 384 -832 896 0 -2048 4352 -4608 0 10240 -21504 22528 0 -49152 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -4 4 4 -20 32 -16 -48 144 -192 64 320 -832 1024 -256 -1792 4352 -5120 1024 9216 -21504 24576 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 0 -8 20 -12 -56 192 -288 80 704 -1920 2496 -448 -5760 14336 -17408 2304 38912 -92160 107520 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 -1 -3 23 -91 271 -627 967 181 -8641 41757 -139657 364229 -703889 605613 2603047 -17860139 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 3 13 67 365 2019 11213 62339 346669 1927971 10722445 59633347 331653869 1844510307 10258341197 |
| Inv | DiagRow1T(n + 1, n) | A016777 | -1 -4 -7 -10 -13 -16 -19 -22 -25 -28 -31 -34 -37 -40 -43 -46 -49 -52 -55 -58 -61 -64 -67 -70 -73 |
| Inv | DiagRow2T(n + 2, n) | A051682 | 1 11 30 58 95 141 196 260 333 415 506 606 715 833 960 1096 1241 1395 1558 1730 1911 2101 2300 2508 |
| Inv | DiagRow3T(n + 3, n) | missing | -1 -26 -102 -256 -515 -906 -1456 -2192 -3141 -4330 -5786 -7536 -9607 -12026 -14820 -18016 -21641 |
| Inv | DiagCol1T(n + 1, 1) | A000295 | 1 -4 11 -26 57 -120 247 -502 1013 -2036 4083 -8178 16369 -32752 65519 -131054 262125 -524268 |
| Inv | DiagCol2T(n + 2, 2) | A045889 | 1 -7 30 -102 303 -825 2116 -5200 12381 -28779 65658 -147594 327835 -721069 1573056 -3408084 7340265 |
| Inv | DiagCol3T(n + 3, 3) | A055583 | 1 -10 58 -256 955 -3178 9740 -28064 77093 -203930 523262 -1309520 3209871 -7731642 18348240 |
| Inv | Polysee docs | missing | 1 -1 1 1 0 1 -1 -2 1 1 1 4 -3 2 1 -1 -4 1 -2 3 1 1 0 5 -4 1 4 1 -1 8 -7 4 -5 6 5 1 1 -16 -3 8 -7 4 |
| Inv | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 |
| Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A123968 | 1 -2 -3 -2 1 6 13 22 33 46 61 78 97 118 141 166 193 222 253 286 321 358 397 438 481 526 573 622 673 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | -1 4 1 -4 -5 4 29 76 151 260 409 604 851 1156 1525 1964 2479 3076 3761 4540 5419 6404 7501 8716 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A077020 | 1 1 -3 1 5 -7 -3 17 -11 -23 45 1 -91 89 93 -271 85 457 -627 -287 1541 -967 -2115 4049 181 -8279 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | A016116 | 1 2 -2 -4 4 8 -8 -16 16 32 -32 -64 64 128 -128 -256 256 512 -512 -1024 1024 2048 -2048 -4096 4096 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -3 -4 -7 -16 253 10352 298321 8420480 248293741 7793136064 261709554889 9405278078208 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -4 1 1 -7 11 -1 1 -10 30 -26 1 1 -13 58 -102 57 -1 1 -16 95 -256 303 -120 1 1 -19 141 -515 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A331969 | 1 -1 1 1 -4 1 -1 11 -7 1 1 -26 30 -10 1 -1 57 -102 58 -13 1 1 -120 303 -256 95 -16 1 -1 247 -825 |
| Inv:Rev | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -5 4 1 47 -37 -11 1 1361 -1072 -316 26 1 -72507 57111 16832 -1380 -57 1 -9100733 7168300 |
| Inv:Rev | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 4 -5 1 -11 -37 47 1 26 -316 -1072 1361 1 -57 -1380 16832 57111 -72507 1 120 -7143 -173222 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A172094 | 1 1 1 3 4 1 11 17 7 1 45 76 40 10 1 197 353 216 72 13 1 903 1688 1145 458 113 16 1 4279 8257 6039 |
| Inv:Rev | Accsee docs | missing | 1 1 0 1 -3 -2 1 -6 5 4 1 -9 21 -5 -4 1 -12 46 -56 1 0 1 -15 80 -176 127 7 8 1 -18 123 -392 563 -262 |
| Inv:Rev | AccRevsee docs | missing | 1 -1 0 1 -3 -2 -1 10 3 4 1 -25 5 -5 -4 -1 56 -46 12 -1 0 1 -119 184 -72 23 7 8 -1 246 -579 376 -139 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 -1 1 -4 1 -7 1 1 -10 11 1 -13 30 -1 1 -16 58 -26 1 -19 95 -102 1 1 -22 141 -256 57 1 -25 196 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -8 3 1 -14 33 -4 1 -20 90 -104 5 1 -26 174 -408 285 -6 1 -32 285 -1024 1515 -720 7 1 -38 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A146559 | 1 0 -2 4 -4 0 8 -16 16 0 -32 64 -64 0 128 -256 256 0 -512 1024 -1024 0 2048 -4096 4096 0 -8192 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 2 12 32 116 400 1344 4624 15760 53792 183744 627200 2141504 7311616 24963072 85229824 290992384 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -4 -8 -36 -116 -392 -1360 -4608 -15760 -53824 -183680 -627264 -2141504 -7311488 -24963328 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A006012 | 1 2 6 20 68 232 792 2704 9232 31520 107616 367424 1254464 4283008 14623104 49926400 170459392 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A006012 | 1 2 6 20 68 232 792 2704 9232 31520 107616 367424 1254464 4283008 14623104 49926400 170459392 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -3 -5 2 17 17 -24 -79 -41 162 333 5 -912 -1251 819 4562 3929 -7255 -20680 -8039 46143 84770 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -4 4 4 -20 32 -16 -48 144 -192 64 320 -832 1024 -256 -1792 4352 -5120 1024 9216 -21504 24576 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 -4 16 -28 20 32 -128 208 -144 -192 768 -1216 832 1024 -4096 6400 -4352 -5120 20480 -31744 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 4 77 390 730626 7368960 188416682025 147187935422220 9210398405098800 867366479041609225319424 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A297382 | 1 1 4 1 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 11 30 102 303 955 3178 9740 32354 106970 333295 1136799 3748104 11877537 40877760 134581692 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -4 -7 30 58 -256 -515 2310 4746 -21504 -44758 204204 428772 -1966080 -4154403 19122246 40599130 |
| Inv:Rev | CentralET(2 n, n) | A091527 | 1 -4 30 -256 2310 -21504 204204 -1966080 19122246 -187432960 1848483780 -18320719872 182327718300 |
| Inv:Rev | CentralOT(2 n + 1, n) | A244469 | 1 -7 58 -515 4746 -44758 428772 -4154403 40599130 -399429602 3950996556 -39255152846 391466112324 |
| Inv:Rev | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -6 12 38 -220 36 2632 -6458 -18924 127724 -48136 -1580836 4343976 11041416 -84673648 49912902 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 10 -56 326 -1952 11908 -73600 459334 -2888192 18268460 -116111360 740945180 -4744192000 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 -2 12 -24 20 24 -112 192 -144 -160 704 -1152 832 896 -3840 6144 -4352 -4608 19456 -30720 21504 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 -4 16 -28 20 32 -128 208 -144 -192 768 -1216 832 1024 -4096 6400 -4352 -5120 20480 -31744 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 0 28 -108 188 -56 -592 1760 -2512 704 5824 -15936 21184 -5760 -43264 113664 -145664 38912 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A077020 | 1 1 -3 1 5 -7 -3 17 -11 -23 45 1 -91 89 93 -271 85 457 -627 -287 1541 -967 -2115 4049 181 -8279 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A052984 | 1 -3 13 -59 269 -1227 5597 -25531 116461 -531243 2423293 -11053979 50423309 -230008587 1049196317 |
| Inv:Rev | DiagRow1T(n + 1, n) | A000295 | 1 -4 11 -26 57 -120 247 -502 1013 -2036 4083 -8178 16369 -32752 65519 -131054 262125 -524268 |
| Inv:Rev | DiagRow2T(n + 2, n) | A045889 | 1 -7 30 -102 303 -825 2116 -5200 12381 -28779 65658 -147594 327835 -721069 1573056 -3408084 7340265 |
| Inv:Rev | DiagRow3T(n + 3, n) | A055583 | 1 -10 58 -256 955 -3178 9740 -28064 77093 -203930 523262 -1309520 3209871 -7731642 18348240 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A016777 | -1 -4 -7 -10 -13 -16 -19 -22 -25 -28 -31 -34 -37 -40 -43 -46 -49 -52 -55 -58 -61 -64 -67 -70 -73 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A051682 | 1 11 30 58 95 141 196 260 333 415 506 606 715 833 960 1096 1241 1395 1558 1730 1911 2101 2300 2508 |
| Inv:Rev | DiagCol3T(n + 3, 3) | missing | -1 -26 -102 -256 -515 -906 -1456 -2192 -3141 -4330 -5786 -7536 -9607 -12026 -14820 -18016 -21641 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 0 1 1 -2 -1 1 1 4 -3 -2 1 1 -4 23 -2 -3 1 1 0 -91 52 1 -4 1 1 8 271 -380 85 6 -5 1 1 -16 |
| Inv:Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 |
| Inv:Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A123968 | 1 -2 -3 -2 1 6 13 22 33 46 61 78 97 118 141 166 193 222 253 286 321 358 397 438 481 526 573 622 673 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 4 23 52 85 116 139 148 137 100 31 -76 -227 -428 -685 -1004 -1391 -1852 -2393 -3020 -3739 -4556 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -1 -3 23 -91 271 -627 967 181 -8641 41757 -139657 364229 -703889 605613 2603047 -17860139 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 -2 52 -380 2104 -9992 42064 -156656 496096 -1148960 261952 18585664 -153400448 892661632 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -3 52 -967 21136 -545747 16493072 -576422831 23017755520 -1038251338979 52346635191104 |
| << | Table | Source | Similars | Index | >> |
Note: The A-numbers are based on a finite number of numerical comparisons. They ignore the sign and the OEIS-offset. Sometimes they differ in the first few values. In such cases, we consider our version to be the better one because it has a common formula as a root. Since the offset of all triangles is 0 also the offset of all sequences is 0.