OEIS Similars: A374439
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A374439 | 1 1 2 1 2 1 1 2 2 2 1 2 3 4 1 1 2 4 6 3 2 1 2 5 8 6 6 1 1 2 6 10 10 12 4 2 1 2 7 12 15 20 10 8 1 1 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A124038 | 1 2 1 1 2 1 2 2 2 1 1 4 3 2 1 2 3 6 4 2 1 1 6 6 8 5 2 1 2 4 12 10 10 6 2 1 1 8 10 20 15 12 7 2 1 2 |
| Std | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A375025 | 1 -2 1 3 -2 1 -4 2 -2 1 6 -2 1 -2 1 -10 5 0 0 -2 1 15 -10 5 2 -1 -2 1 -20 10 -12 6 4 -2 -2 1 30 -8 |
| Std | Accsee docs | missing | 1 1 3 1 3 4 1 3 5 7 1 3 6 10 11 1 3 7 13 16 18 1 3 8 16 22 28 29 1 3 9 19 29 41 45 47 1 3 10 22 37 |
| Std | AccRevsee docs | missing | 1 2 3 1 3 4 2 4 6 7 1 5 8 10 11 2 5 11 15 17 18 1 7 13 21 26 28 29 2 6 18 28 38 44 46 47 1 9 19 39 |
| Std | AntiDiagsee docs | missing | 1 1 1 2 1 2 1 2 1 1 2 2 1 2 3 2 1 2 4 4 1 2 5 6 1 1 2 6 8 3 1 2 7 10 6 2 1 2 8 12 10 6 1 2 9 14 15 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 4 1 4 3 1 4 6 8 1 4 9 16 5 1 4 12 24 15 12 1 4 15 32 30 36 7 1 4 18 40 50 72 28 16 1 4 21 48 75 |
| Std | RowSum∑ k=0..n T(n, k) | A000032 | 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603 64079 103682 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A000045 | 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A006355 | 0 2 2 4 6 10 16 26 42 68 110 178 288 466 754 1220 1974 3194 5168 8362 13530 21892 35422 57314 92736 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A000045 | 1 -1 0 -1 -1 -2 -3 -5 -8 -13 -21 -34 -55 -89 -144 -233 -377 -610 -987 -1597 -2584 -4181 -6765 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000032 | 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603 64079 103682 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 3 3 4 5 8 11 15 20 28 39 54 74 102 141 195 269 371 512 707 976 1347 1859 2566 3542 4889 6748 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 4 8 16 31 58 107 194 348 618 1089 1906 3317 5744 9904 17012 29123 49706 84607 143662 243396 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 5 8 19 35 68 125 229 412 735 1299 2280 3977 6901 11920 20507 35155 60076 102373 174005 295076 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 2 2 2 12 12 120 60 840 840 5040 2520 55440 27720 720720 360360 720720 720720 24504480 12252240 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A297382 | 1 2 2 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 1 |
| Std | RowMaxMax k=0..n | T(n, k) | | missing | 1 2 2 2 4 6 8 12 20 30 42 70 112 168 252 420 660 990 1584 2574 4004 6006 10010 16016 24752 38896 |
| Std | ColMiddleT(n, n // 2) | missing | 1 1 2 2 3 4 8 10 15 21 42 56 84 120 240 330 495 715 1430 2002 3003 4368 8736 12376 18564 27132 |
| Std | CentralET(2 n, n) | missing | 1 2 3 8 15 42 84 240 495 1430 3003 8736 18564 54264 116280 341088 735471 2163150 4686825 13813800 |
| Std | CentralOT(2 n + 1, n) | missing | 1 2 4 10 21 56 120 330 715 2002 4368 12376 27132 77520 170544 490314 1081575 3124550 6906900 |
| Std | 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 |
| Std | ColRightT(n, n) | A000034 | 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 |
| Std | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 3 6 15 44 128 375 1123 3400 10356 31736 97760 302351 938265 2920182 9111455 28491504 89264640 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 -2 1 -4 16 -41 113 -344 1036 -3112 9472 -29041 89363 -276082 856081 -2662352 8300608 -25937564 |
| Std | TransNat0∑ k=0..n T(n, k) k | missing | 0 2 4 12 24 50 96 182 336 612 1100 1958 3456 6058 10556 18300 31584 54298 93024 158878 270600 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 5 8 19 35 68 125 229 412 735 1299 2280 3977 6901 11920 20507 35155 60076 102373 174005 295076 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 2 6 28 66 170 376 818 1694 3428 6770 13138 25104 47362 88374 163340 299394 544762 984776 1769842 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A048654 | 1 4 9 22 53 128 309 746 1801 4348 10497 25342 61181 147704 356589 860882 2078353 5017588 12113529 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000129 | 1 0 1 -2 5 -12 29 -70 169 -408 985 -2378 5741 -13860 33461 -80782 195025 -470832 1136689 -2744210 |
| Std | DiagRow1T(n + 1, n) | A029578 | 1 2 2 4 3 6 4 8 5 10 6 12 7 14 8 16 9 18 10 20 11 22 12 24 13 26 14 28 15 30 16 32 17 34 18 36 19 |
| Std | DiagRow2T(n + 2, n) | A131259 | 1 2 3 6 6 12 10 20 15 30 21 42 28 56 36 72 45 90 55 110 66 132 78 156 91 182 105 210 120 240 136 |
| Std | DiagRow3T(n + 3, n) | missing | 1 2 4 8 10 20 20 40 35 70 56 112 84 168 120 240 165 330 220 440 286 572 364 728 455 910 560 1120 |
| Std | DiagCol1T(n + 1, 1) | A055642 | 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 |
| Std | DiagCol2T(n + 2, 2) | 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 | DiagCol3T(n + 3, 3) | A005843 | 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 |
| Std | Polysee docs | missing | 1 1 1 1 3 1 1 4 5 1 1 7 9 7 1 1 11 29 16 9 1 1 18 65 79 25 11 1 1 29 181 223 169 36 13 1 1 47 441 |
| Std | PolyRow1∑ k=0..1 T(1, k) n^k | A005408 | 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 |
| Std | PolyRow2∑ k=0..2 T(2, k) n^k | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 7 29 79 169 311 517 799 1169 1639 2221 2927 3769 4759 5909 7231 8737 10439 12349 14479 16841 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A006131 | 1 5 9 29 65 181 441 1165 2929 7589 19305 49661 126881 325525 833049 2135149 5467345 14007941 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 7 16 79 223 934 2941 11347 37816 139939 480283 1739734 6062281 21719887 76280416 271759399 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 3 9 79 569 8986 103009 2347115 36899281 1098282907 21939496921 805961760902 19528031758921 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A374439 | 1 1 -2 1 -2 1 1 -2 2 -2 1 -2 3 -4 1 1 -2 4 -6 3 -2 1 -2 5 -8 6 -6 1 1 -2 6 -10 10 -12 4 -2 1 -2 7 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A124038 | 1 -2 1 1 -2 1 -2 2 -2 1 1 -4 3 -2 1 -2 3 -6 4 -2 1 1 -6 6 -8 5 -2 1 -2 4 -12 10 -10 6 -2 1 1 -8 10 |
| Alt | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A375025 | 1 2 1 3 2 1 4 2 2 1 6 2 1 2 1 10 5 0 0 2 1 15 10 5 -2 -1 2 1 20 10 12 6 -4 -2 2 1 30 8 4 16 8 -6 -3 |
| Alt | Accsee docs | missing | 1 1 -1 1 -1 0 1 -1 1 -1 1 -1 2 -2 -1 1 -1 3 -3 0 -2 1 -1 4 -4 2 -4 -3 1 -1 5 -5 5 -7 -3 -5 1 -1 6 |
| Alt | AccRevsee docs | missing | 1 -2 -1 1 -1 0 -2 0 -2 -1 1 -3 0 -2 -1 -2 1 -5 -1 -3 -2 1 -5 1 -7 -2 -4 -3 -2 2 -10 0 -10 -4 -6 -5 |
| Alt | AntiDiagsee docs | missing | 1 1 1 -2 1 -2 1 -2 1 1 -2 2 1 -2 3 -2 1 -2 4 -4 1 -2 5 -6 1 1 -2 6 -8 3 1 -2 7 -10 6 -2 1 -2 8 -12 |
| Alt | RowSum∑ k=0..n T(n, k) | A000045 | 1 -1 0 -1 -1 -2 -3 -5 -8 -13 -21 -34 -55 -89 -144 -233 -377 -610 -987 -1597 -2584 -4181 -6765 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A000045 | 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A006355 | 0 -2 -2 -4 -6 -10 -16 -26 -42 -68 -110 -178 -288 -466 -754 -1220 -1974 -3194 -5168 -8362 -13530 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000032 | 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603 64079 103682 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000032 | 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603 64079 103682 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 -1 -1 0 1 0 -1 -1 0 0 -1 -2 -2 -2 -3 -5 -7 -9 -12 -17 -24 -33 -45 -62 -86 -119 -164 -226 -312 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A001629 | 1 0 0 0 -1 -2 -5 -10 -20 -38 -71 -130 -235 -420 -744 -1308 -2285 -3970 -6865 -11822 -20284 -34690 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -3 0 -5 -5 -12 -19 -35 -60 -105 -181 -312 -535 -915 -1560 -2653 -4501 -7620 -12875 -21715 -36564 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 2 2 2 12 12 120 60 840 840 5040 2520 55440 27720 720720 360360 720720 720720 24504480 12252240 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A297382 | 1 2 2 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 1 |
| Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 2 2 2 4 6 8 12 20 30 42 70 112 168 252 420 660 990 1584 2574 4004 6006 10010 16016 24752 38896 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 1 -2 -2 3 4 -8 -10 15 21 -42 -56 84 120 -240 -330 495 715 -1430 -2002 3003 4368 -8736 -12376 |
| Alt | CentralET(2 n, n) | missing | 1 -2 3 -8 15 -42 84 -240 495 -1430 3003 -8736 18564 -54264 116280 -341088 735471 -2163150 4686825 |
| Alt | CentralOT(2 n + 1, n) | missing | 1 -2 4 -10 21 -56 120 -330 715 -2002 4368 -12376 27132 -77520 170544 -490314 1081575 -3124550 |
| Alt | 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 |
| Alt | ColRightT(n, n) | A000034 | 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 1 -2 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 -1 -2 -1 -4 -16 -41 -113 -344 -1036 -3112 -9472 -29041 -89363 -276082 -856081 -2662352 -8300608 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -3 6 -15 44 -128 375 -1123 3400 -10356 31736 -97760 302351 -938265 2920182 -9111455 28491504 |
| Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 -2 0 -4 -4 -10 -16 -30 -52 -92 -160 -278 -480 -826 -1416 -2420 -4124 -7010 -11888 -20118 -33980 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -3 0 -5 -5 -12 -19 -35 -60 -105 -181 -312 -535 -915 -1560 -2653 -4501 -7620 -12875 -21715 -36564 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -2 2 -12 -10 -42 -72 -162 -310 -612 -1162 -2194 -4080 -7522 -13742 -24924 -44906 -80442 -143352 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000129 | 1 0 1 2 5 12 29 70 169 408 985 2378 5741 13860 33461 80782 195025 470832 1136689 2744210 6625109 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A048654 | 1 -4 9 -22 53 -128 309 -746 1801 -4348 10497 -25342 61181 -147704 356589 -860882 2078353 -5017588 |
| Alt | DiagRow1T(n + 1, n) | A029578 | 1 -2 2 -4 3 -6 4 -8 5 -10 6 -12 7 -14 8 -16 9 -18 10 -20 11 -22 12 -24 13 -26 14 -28 15 -30 16 -32 |
| Alt | DiagRow2T(n + 2, n) | A131259 | 1 -2 3 -6 6 -12 10 -20 15 -30 21 -42 28 -56 36 -72 45 -90 55 -110 66 -132 78 -156 91 -182 105 -210 |
| Alt | DiagRow3T(n + 3, n) | missing | 1 -2 4 -8 10 -20 20 -40 35 -70 56 -112 84 -168 120 -240 165 -330 220 -440 286 -572 364 -728 455 |
| Alt | DiagCol1T(n + 1, 1) | A055642 | -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 |
| Alt | DiagCol2T(n + 2, 2) | 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 |
| Alt | DiagCol3T(n + 3, 3) | A005843 | -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -28 -30 -32 -34 -36 -38 -40 -42 -44 -46 -48 -50 -52 |
| Alt | Polysee docs | missing | 1 1 1 1 -1 1 1 0 -3 1 1 -1 1 -5 1 1 -1 -11 4 -7 1 1 -2 -7 -41 9 -9 1 1 -3 -51 -5 -103 16 -11 1 1 -5 |
| Alt | PolyRow1∑ k=0..1 T(1, k) n^k | A005408 | 1 -1 -3 -5 -7 -9 -11 -13 -15 -17 -19 -21 -23 -25 -27 -29 -31 -33 -35 -37 -39 -41 -43 -45 -47 -49 |
| Alt | PolyRow2∑ k=0..2 T(2, k) n^k | A000290 | 1 0 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 -1 -11 -41 -103 -209 -371 -601 -911 -1313 -1819 -2441 -3191 -4081 -5123 -6329 -7711 -9281 -11051 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -3 1 -11 -7 -51 -79 -283 -599 -1731 -4127 -11051 -27559 -71763 -181999 -469051 -1197047 -3073251 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -5 4 -41 -5 -374 -419 -3785 -7556 -41621 -109625 -484214 -1470839 -5828765 -19066316 -71525201 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 -1 1 -41 41 -5034 6217 -1357313 2021809 -646281197 1131064881 -479508072614 965399387161 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A124038 | 1 2 1 1 2 1 2 2 2 1 1 4 3 2 1 2 3 6 4 2 1 1 6 6 8 5 2 1 2 4 12 10 10 6 2 1 1 8 10 20 15 12 7 2 1 2 |
| Rev | InvT-1(n, k), 0 ≤ k ≤ n | A375025 | 1 -2 1 3 -2 1 -4 2 -2 1 6 -2 1 -2 1 -10 5 0 0 -2 1 15 -10 5 2 -1 -2 1 -20 10 -12 6 4 -2 -2 1 30 -8 |
| Rev | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -2 1 -2 3 1 -2 2 -4 1 -2 1 -2 6 1 -2 0 0 5 -10 1 -2 -1 2 5 -10 15 1 -2 -2 4 6 -12 10 -20 1 -2 |
| Rev | Accsee docs | missing | 1 2 3 1 3 4 2 4 6 7 1 5 8 10 11 2 5 11 15 17 18 1 7 13 21 26 28 29 2 6 18 28 38 44 46 47 1 9 19 39 |
| Rev | AccRevsee docs | missing | 1 1 3 1 3 4 1 3 5 7 1 3 6 10 11 1 3 7 13 16 18 1 3 8 16 22 28 29 1 3 9 19 29 41 45 47 1 3 10 22 37 |
| Rev | AntiDiagsee docs | missing | 1 2 1 1 2 2 1 2 1 2 4 2 1 3 3 1 2 6 6 2 1 4 6 4 1 2 8 12 8 2 1 5 10 10 5 1 2 10 20 20 10 2 1 6 15 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 2 2 1 4 3 2 4 6 4 1 8 9 8 5 2 6 18 16 10 6 1 12 18 32 25 12 7 2 8 36 40 50 36 14 8 1 16 30 80 75 |
| Rev | RowSum∑ k=0..n T(n, k) | A000032 | 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603 64079 103682 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A133585 | 1 2 2 4 5 10 13 26 34 68 89 178 233 466 610 1220 1597 3194 4181 8362 10946 21892 28657 57314 75025 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A133586 | 0 1 2 3 6 8 16 21 42 55 110 144 288 377 754 987 1974 2584 5168 6765 13530 17711 35422 46368 92736 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000045 | 1 1 0 1 -1 2 -3 5 -8 13 -21 34 -55 89 -144 233 -377 610 -987 1597 -2584 4181 -6765 10946 -17711 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000032 | 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603 64079 103682 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, 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 8192 8192 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 5 8 19 35 68 125 229 412 735 1299 2280 3977 6901 11920 20507 35155 60076 102373 174005 295076 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 4 8 16 31 58 107 194 348 618 1089 1906 3317 5744 9904 17012 29123 49706 84607 143662 243396 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 2 2 2 12 12 120 60 840 840 5040 2520 55440 27720 720720 360360 720720 720720 24504480 12252240 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A297382 | 1 2 2 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 1 |
| Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 2 2 2 4 6 8 12 20 30 42 70 112 168 252 420 660 990 1584 2574 4004 6006 10010 16016 24752 38896 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 2 2 2 3 6 8 10 15 30 42 56 84 168 240 330 495 990 1430 2002 3003 6006 8736 12376 18564 37128 |
| Rev | CentralET(2 n, n) | missing | 1 2 3 8 15 42 84 240 495 1430 3003 8736 18564 54264 116280 341088 735471 2163150 4686825 13813800 |
| Rev | CentralOT(2 n + 1, n) | missing | 2 2 6 10 30 56 168 330 990 2002 6006 12376 37128 77520 232560 490314 1470942 3124550 9373650 |
| Rev | ColLeftT(n, 0) | A000034 | 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 |
| Rev | 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 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 3 6 15 44 128 375 1123 3400 10356 31736 97760 302351 938265 2920182 9111455 28491504 89264640 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 -2 -1 -4 -16 -41 -113 -344 -1036 -3112 -9472 -29041 -89363 -276082 -856081 -2662352 -8300608 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A023607 | 0 1 4 9 20 40 78 147 272 495 890 1584 2796 4901 8540 14805 25552 43928 75258 128535 218920 371931 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 4 8 16 31 58 107 194 348 618 1089 1906 3317 5744 9904 17012 29123 49706 84607 143662 243396 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 6 19 50 120 268 573 1182 2375 4670 9024 17184 32321 60150 110915 202882 368472 664988 1193325 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A006131 | 1 5 9 29 65 181 441 1165 2929 7589 19305 49661 126881 325525 833049 2135149 5467345 14007941 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -3 1 -11 -7 -51 -79 -283 -599 -1731 -4127 -11051 -27559 -71763 -181999 -469051 -1197047 -3073251 |
| Rev | DiagRow1T(n + 1, n) | A055642 | 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 |
| Rev | DiagRow2T(n + 2, n) | 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 | DiagRow3T(n + 3, n) | A005843 | 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 |
| Rev | DiagCol1T(n + 1, 1) | A029578 | 1 2 2 4 3 6 4 8 5 10 6 12 7 14 8 16 9 18 10 20 11 22 12 24 13 26 14 28 15 30 16 32 17 34 18 36 19 |
| Rev | DiagCol2T(n + 2, 2) | A131259 | 1 2 3 6 6 12 10 20 15 30 21 42 28 56 36 72 45 90 55 110 66 132 78 156 91 182 105 210 120 240 136 |
| Rev | DiagCol3T(n + 3, 3) | missing | 1 2 4 8 10 20 20 40 35 70 56 112 84 168 120 240 165 330 220 440 286 572 364 728 455 910 560 1120 |
| Rev | Polysee docs | missing | 1 2 1 1 3 1 2 4 4 1 1 7 9 5 1 2 11 22 16 6 1 1 18 53 53 25 7 1 2 29 128 175 106 36 8 1 1 47 309 578 |
| Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 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 37 |
| Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A188377 | 2 7 22 53 106 187 302 457 658 911 1222 1597 2042 2563 3166 3857 4642 5527 6518 7621 8842 10187 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A048654 | 1 4 9 22 53 128 309 746 1801 4348 10497 25342 61181 147704 356589 860882 2078353 5017588 12113529 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A108300 | 1 5 16 53 175 578 1909 6305 20824 68777 227155 750242 2477881 8183885 27029536 89272493 294847015 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 3 9 53 449 5042 70669 1187741 23272129 520670963 13092591601 365435296162 11208613137121 |
| Rev:Inv | TriangleT(n, k), 0 ≤ k ≤ n | A375025 | 1 -2 1 3 -2 1 -4 2 -2 1 6 -2 1 -2 1 -10 5 0 0 -2 1 15 -10 5 2 -1 -2 1 -20 10 -12 6 4 -2 -2 1 30 -8 |
| Rev:Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -2 1 -2 3 1 -2 2 -4 1 -2 1 -2 6 1 -2 0 0 5 -10 1 -2 -1 2 5 -10 15 1 -2 -2 4 6 -12 10 -20 1 -2 |
| Rev:Inv | InvT-1(n, k), 0 ≤ k ≤ n | A124038 | 1 2 1 1 2 1 2 2 2 1 1 4 3 2 1 2 3 6 4 2 1 1 6 6 8 5 2 1 2 4 12 10 10 6 2 1 1 8 10 20 15 12 7 2 1 2 |
| Rev:Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A374439 | 1 1 2 1 2 1 1 2 2 2 1 2 3 4 1 1 2 4 6 3 2 1 2 5 8 6 6 1 1 2 6 10 10 12 4 2 1 2 7 12 15 20 10 8 1 1 |
| Rev:Inv | Accsee docs | missing | 1 -2 -1 3 1 2 -4 -2 -4 -3 6 4 5 3 4 -10 -5 -5 -5 -7 -6 15 5 10 12 11 9 10 -20 -10 -22 -16 -12 -14 |
| Rev:Inv | AccRevsee docs | missing | 1 1 -1 1 -1 2 1 -1 1 -3 1 -1 0 -2 4 1 -1 -1 -1 4 -6 1 -1 -2 0 5 -5 10 1 -1 -3 1 7 -5 5 -15 1 -1 -4 |
| Rev:Inv | AntiDiagsee docs | missing | 1 -2 3 1 -4 -2 6 2 1 -10 -2 -2 15 5 1 1 -20 -10 0 -2 30 10 5 0 1 -52 -8 -12 2 -2 78 26 4 6 -1 1 -96 |
| Rev:Inv | Diffx1T(n, k) (k+1) | missing | 1 -2 2 3 -4 3 -4 4 -6 4 6 -4 3 -8 5 -10 10 0 0 -10 6 15 -20 15 8 -5 -12 7 -20 20 -36 24 20 -12 -14 |
| Rev:Inv | RowSum∑ k=0..n T(n, k) | A086990 | 1 -1 2 -3 4 -6 10 -15 20 -30 52 -78 96 -144 282 -423 420 -630 1660 -2490 1304 -1956 11332 -16998 |
| Rev:Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 -2 4 -6 8 -12 20 -30 40 -60 104 -156 192 -288 564 -846 840 -1260 3320 -4980 2608 -3912 22664 |
| Rev:Inv | OddSum∑ k=0..n T(n, k) odd(k) | A086990 | 0 1 -2 3 -4 6 -10 15 -20 30 -52 78 -96 144 -282 423 -420 630 -1660 2490 -1304 1956 -11332 16998 |
| Rev:Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A375026 | 1 -3 6 -9 12 -18 30 -45 60 -90 156 -234 288 -432 846 -1269 1260 -1890 4980 -7470 3912 -5868 33996 |
| Rev:Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 3 6 9 12 18 36 57 78 138 276 450 630 1368 2736 4617 7974 16578 33156 57774 111636 225228 450456 |
| Rev:Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 -2 4 -6 9 -14 22 -32 46 -72 114 -162 225 -366 606 -816 1038 -1868 3424 -4076 3994 -9660 21828 |
| Rev:Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -3 6 -13 22 -38 72 -125 190 -310 580 -962 1308 -2064 4236 -6909 7566 -11550 31140 -50630 31060 |
| Rev:Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 0 2 -2 2 -4 8 -10 10 -20 44 -52 36 -96 276 -282 -6 -420 2060 -1660 -2372 -1304 18752 -11332 |
| Rev:Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 2 6 4 6 10 30 60 240 1144 780 1440 327600 176814000 3543072957846 531150900 37992200400 |
| Rev:Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 2 1 2 2 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 1 |
| Rev:Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 2 3 4 6 10 15 20 30 52 78 96 150 282 426 820 1616 3032 5368 10416 19440 38580 72540 137680 266698 |
| Rev:Inv | ColMiddleT(n, n // 2) | missing | 1 -2 -2 2 1 0 2 6 8 -22 -30 -30 -50 152 218 310 460 -1320 -1840 -2748 -3999 11328 15678 24762 35396 |
| Rev:Inv | CentralET(2 n, n) | missing | 1 -2 1 2 8 -30 -50 218 460 -1840 -3999 15678 35396 -136340 -315300 1200330 2827260 -10668888 |
| Rev:Inv | CentralOT(2 n + 1, n) | missing | -2 2 0 6 -22 -30 152 310 -1320 -2748 11328 24762 -99140 -223060 876600 2016630 -7817112 -18291720 |
| Rev:Inv | ColLeftT(n, 0) | A086990 | 1 -2 3 -4 6 -10 15 -20 30 -52 78 -96 144 -282 423 -420 630 -1660 2490 -1304 1956 -11332 16998 3896 |
| Rev: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 |
| Rev:Inv | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 -1 0 -3 -3 6 44 93 -21 -741 -2176 -1404 11676 47312 62292 -158003 -970137 -1883355 1375184 |
| Rev:Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 3 8 17 29 46 108 385 1259 3023 4584 2132 -4324 22032 215924 769617 1378151 -139439 -7853016 |
| Rev:Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 0 1 -2 2 -2 5 -10 10 -8 26 -60 48 -6 141 -426 210 400 830 -3676 652 7420 5666 -37892 -1948 |
| Rev:Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 0 2 -2 2 -4 8 -10 10 -20 44 -52 36 -96 276 -282 -6 -420 2060 -1660 -2372 -1304 18752 -11332 |
| Rev:Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 2 3 0 -2 -2 7 0 -10 -12 46 8 -96 -90 399 144 -1074 -820 4090 2016 -12748 -8724 46678 26560 |
| Rev:Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000244 | 1 -3 9 -27 81 -243 729 -2187 6561 -19683 59049 -177147 531441 -1594323 4782969 -14348907 43046721 |
| Rev:Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 5 17 45 121 405 1345 3645 9545 32805 114577 295245 687129 2657205 10509537 23914845 38355945 |
| Rev:Inv | DiagRow1T(n + 1, n) | A055642 | -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 |
| Rev:Inv | DiagRow2T(n + 2, n) | A001477 | 3 2 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 |
| Rev:Inv | DiagRow3T(n + 3, n) | A005843 | -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 |
| Rev:Inv | DiagCol1T(n + 1, 1) | missing | 1 -2 2 -2 5 -10 10 -8 26 -60 48 -6 141 -426 210 400 830 -3676 652 7420 5666 -37892 -1948 106928 |
| Rev:Inv | DiagCol2T(n + 2, 2) | missing | 1 -2 1 0 5 -12 4 8 30 -90 3 144 213 -820 -200 2016 1838 -8724 -3710 26560 18946 -103032 -53464 |
| Rev:Inv | DiagCol3T(n + 3, 3) | missing | 1 -2 0 2 6 -16 -4 30 45 -150 -72 394 410 -1616 -1008 5048 4362 -19140 -13280 65140 51516 -240712 |
| Rev:Inv | Polysee docs | missing | 1 -2 1 3 -1 1 -4 2 0 1 6 -3 3 1 1 -10 4 0 6 2 1 15 -6 6 11 11 3 1 -20 10 0 36 36 18 4 1 30 -15 15 |
| Rev:Inv | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | -2 -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 |
| Rev:Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A059100 | 3 2 3 6 11 18 27 38 51 66 83 102 123 146 171 198 227 258 291 326 363 402 443 486 531 578 627 678 |
| Rev:Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | -4 -3 0 11 36 81 152 255 396 581 816 1107 1460 1881 2376 2951 3612 4365 5216 6171 7236 8417 9720 |
| Rev:Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A126982 | 1 0 3 0 6 0 15 0 30 0 78 0 144 0 423 0 630 0 2490 0 1956 0 16998 0 -5844 0 142860 0 -235740 0 |
| Rev:Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 6 11 36 86 246 631 1716 4526 12156 32286 86256 229776 613206 1634511 4359396 11624006 31000116 |
| Rev:Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 -1 3 11 142 1890 30375 565755 12017886 286949810 7611882478 222176419182 7078092232824 |
| << | 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.