OEIS Similars: A064189, A026300, A009766
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A064189 | 1 1 1 2 2 1 4 5 3 1 9 12 9 4 1 21 30 25 14 5 1 51 76 69 44 20 6 1 127 196 189 133 70 27 7 1 323 512 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A026300 | 1 1 1 1 2 2 1 3 5 4 1 4 9 12 9 1 5 14 25 30 21 1 6 20 44 69 76 51 1 7 27 70 133 189 196 127 1 8 35 |
| Std | Accsee docs | missing | 1 1 2 2 4 5 4 9 12 13 9 21 30 34 35 21 51 76 90 95 96 51 127 196 240 260 266 267 127 323 512 645 |
| Std | AccRevsee docs | missing | 1 1 2 1 3 5 1 4 9 13 1 5 14 26 35 1 6 20 45 75 96 1 7 27 71 140 216 267 1 8 35 105 238 427 623 750 |
| Std | AntiDiagsee docs | A106489 | 1 1 2 1 4 2 9 5 1 21 12 3 51 30 9 1 127 76 25 4 323 196 69 14 1 835 512 189 44 5 2188 1353 518 133 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 2 4 3 4 10 9 4 9 24 27 16 5 21 60 75 56 25 6 51 152 207 176 100 36 7 127 392 567 532 350 162 |
| Std | RowSum∑ k=0..n T(n, k) | A005773 | 1 2 5 13 35 96 267 750 2123 6046 17303 49721 143365 414584 1201917 3492117 10165779 29643870 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A002426 | 1 1 3 7 19 51 141 393 1107 3139 8953 25653 73789 212941 616227 1787607 5196627 15134931 44152809 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A005717 | 0 1 2 6 16 45 126 357 1016 2907 8350 24068 69576 201643 585690 1704510 4969152 14508939 42422022 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A005043 | 1 0 1 1 3 6 15 36 91 232 603 1585 4213 11298 30537 83097 227475 625992 1730787 4805595 13393689 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A005773 | 1 2 5 13 35 96 267 750 2123 6046 17303 49721 143365 414584 1201917 3492117 10165779 29643870 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A005043 | 1 1 3 6 15 36 91 232 603 1585 4213 11298 30537 83097 227475 625992 1730787 4805595 13393689 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A026943 | 1 3 11 38 129 429 1407 4563 14669 46823 148587 469226 1475669 4624437 14447703 45017082 139937301 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 60 36 1050 4903140 63847980 448240898560 10968190265340 203258629623949200 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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) | | A026938 | 1 1 2 5 12 30 76 196 518 1422 3915 10813 29964 83304 232323 649845 1822824 5147328 14727168 |
| Std | ColMiddleT(n, n // 2) | A344394 | 1 1 2 5 9 25 44 133 230 726 1242 4037 6853 22737 38376 129285 217242 740554 1239980 4266830 7123765 |
| Std | CentralET(2 n, n) | A026302 | 1 2 9 44 230 1242 6853 38376 217242 1239980 7123765 41141916 238637282 1389206210 8112107475 |
| Std | CentralOT(2 n + 1, n) | A344396 | 1 5 25 133 726 4037 22737 129285 740554 4266830 24701425 143567173 837212650 4896136845 28703894775 |
| Std | ColLeftT(n, 0) | A001006 | 1 1 2 4 9 21 51 127 323 835 2188 5798 15511 41835 113634 310572 853467 2356779 6536382 18199284 |
| 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) | A344502 | 1 2 7 29 128 587 2759 13190 63844 311948 1535488 7602971 37829455 188989166 947399951 4763280965 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344503 | 1 0 -1 3 0 -5 15 0 -28 84 0 -165 495 0 -1001 3003 0 -6188 18564 0 -38760 116280 0 -245157 735471 0 |
| Std | TransNat0∑ k=0..n T(n, k) k | A330796 | 0 1 4 14 46 147 462 1437 4438 13637 41746 127426 388076 1179739 3581052 10856790 32880942 99496293 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | A344504 | 0 1 6 26 100 361 1254 4245 14108 46247 149998 482412 1540880 4893859 15468910 48696930 152764452 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A330799 | 1 3 13 59 285 1419 7245 37659 198589 1059371 5705517 30976571 169338781 931239243 5147825421 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A330800 | 1 -1 5 -17 77 -345 1653 -8097 40733 -208553 1084421 -5708785 30370861 -163019641 881790357 |
| Std | DiagRow1T(n + 1, 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 |
| Std | DiagRow2T(n + 2, n) | A000096 | 2 5 9 14 20 27 35 44 54 65 77 90 104 119 135 152 170 189 209 230 252 275 299 324 350 377 405 434 |
| Std | DiagRow3T(n + 3, n) | A000297 | 4 12 25 44 70 104 147 200 264 340 429 532 650 784 935 1104 1292 1500 1729 1980 2254 2552 2875 3224 |
| Std | DiagCol1T(n + 1, 1) | A002026 | 1 2 5 12 30 76 196 512 1353 3610 9713 26324 71799 196938 542895 1503312 4179603 11662902 32652735 |
| Std | DiagCol2T(n + 2, 2) | A005322 | 1 3 9 25 69 189 518 1422 3915 10813 29964 83304 232323 649845 1822824 5126520 14453451 40843521 |
| Std | DiagCol3T(n + 3, 3) | A005323 | 1 4 14 44 133 392 1140 3288 9438 27016 77220 220584 630084 1800384 5147328 14727168 42171849 |
| Std | Polysee docs | A330792 | 1 1 1 2 2 1 4 5 3 1 9 13 10 4 1 21 35 34 17 5 1 51 96 117 73 26 6 1 127 267 405 315 136 37 7 1 323 |
| 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 | A002522 | 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | A135859 | 4 13 34 73 136 229 358 529 748 1021 1354 1753 2224 2773 3406 4129 4948 5869 6898 8041 9304 10693 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A059738 | 1 3 10 34 117 405 1407 4899 17083 59629 208284 727900 2544751 8898873 31125138 108881166 380928795 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A344506 | 1 4 17 73 315 1362 5895 25528 110579 479068 2075683 8993897 38971621 168871854 731764089 3170939841 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 10 73 713 8796 131727 2325324 47317699 1090925062 28110267788 800653100281 24980114328391 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A064189 | 1 1 -1 2 -2 1 4 -5 3 -1 9 -12 9 -4 1 21 -30 25 -14 5 -1 51 -76 69 -44 20 -6 1 127 -196 189 -133 70 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A026300 | 1 -1 1 1 -2 2 -1 3 -5 4 1 -4 9 -12 9 -1 5 -14 25 -30 21 1 -6 20 -44 69 -76 51 -1 7 -27 70 -133 189 |
| Alt | Accsee docs | missing | 1 1 0 2 0 1 4 -1 2 1 9 -3 6 2 3 21 -9 16 2 7 6 51 -25 44 0 20 14 15 127 -69 120 -13 57 30 37 36 323 |
| Alt | AntiDiagsee docs | A106489 | 1 1 2 -1 4 -2 9 -5 1 21 -12 3 51 -30 9 -1 127 -76 25 -4 323 -196 69 -14 1 835 -512 189 -44 5 2188 |
| Alt | RowSum∑ k=0..n T(n, k) | A005043 | 1 0 1 1 3 6 15 36 91 232 603 1585 4213 11298 30537 83097 227475 625992 1730787 4805595 13393689 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A002426 | 1 1 3 7 19 51 141 393 1107 3139 8953 25653 73789 212941 616227 1787607 5196627 15134931 44152809 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A005717 | 0 -1 -2 -6 -16 -45 -126 -357 -1016 -2907 -8350 -24068 -69576 -201643 -585690 -1704510 -4969152 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A005773 | 1 2 5 13 35 96 267 750 2123 6046 17303 49721 143365 414584 1201917 3492117 10165779 29643870 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A005773 | 1 2 5 13 35 96 267 750 2123 6046 17303 49721 143365 414584 1201917 3492117 10165779 29643870 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A089372 | 1 1 1 2 5 12 29 72 183 473 1239 3282 8777 23665 64261 175584 482395 1331795 3692891 10280190 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 3 6 17 43 119 325 909 2553 7235 20606 58981 169471 488591 1412650 4094549 11893849 34615739 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 60 36 1050 4903140 63847980 448240898560 10968190265340 203258629623949200 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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) | | A026938 | 1 1 2 5 12 30 76 196 518 1422 3915 10813 29964 83304 232323 649845 1822824 5147328 14727168 |
| Alt | ColMiddleT(n, n // 2) | A344394 | 1 1 -2 -5 9 25 -44 -133 230 726 -1242 -4037 6853 22737 -38376 -129285 217242 740554 -1239980 |
| Alt | CentralET(2 n, n) | A026302 | 1 -2 9 -44 230 -1242 6853 -38376 217242 -1239980 7123765 -41141916 238637282 -1389206210 8112107475 |
| Alt | CentralOT(2 n + 1, n) | A344396 | 1 -5 25 -133 726 -4037 22737 -129285 740554 -4266830 24701425 -143567173 837212650 -4896136845 |
| Alt | ColLeftT(n, 0) | A001006 | 1 1 2 4 9 21 51 127 323 835 2188 5798 15511 41835 113634 310572 853467 2356779 6536382 18199284 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | A344503 | 1 0 -1 -3 0 5 15 0 -28 -84 0 165 495 0 -1001 -3003 0 6188 18564 0 -38760 -116280 0 245157 735471 0 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344502 | 1 -2 7 -29 128 -587 2759 -13190 63844 -311948 1535488 -7602971 37829455 -188989166 947399951 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A187306 | 0 -1 0 -2 -2 -7 -14 -37 -90 -233 -602 -1586 -4212 -11299 -30536 -83098 -227474 -625993 -1730786 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 2 -2 4 -1 10 11 44 97 274 708 1920 5165 14074 38486 105892 292625 812170 2262638 6325456 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A330800 | 1 1 5 17 77 345 1653 8097 40733 208553 1084421 5708785 30370861 163019641 881790357 4801746753 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A330799 | 1 -3 13 -59 285 -1419 7245 -37659 198589 -1059371 5705517 -30976571 169338781 -931239243 5147825421 |
| Alt | DiagRow1T(n + 1, 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 |
| Alt | DiagRow2T(n + 2, n) | A000096 | 2 -5 9 -14 20 -27 35 -44 54 -65 77 -90 104 -119 135 -152 170 -189 209 -230 252 -275 299 -324 350 |
| Alt | DiagRow3T(n + 3, n) | A000297 | 4 -12 25 -44 70 -104 147 -200 264 -340 429 -532 650 -784 935 -1104 1292 -1500 1729 -1980 2254 -2552 |
| Alt | DiagCol1T(n + 1, 1) | A002026 | -1 -2 -5 -12 -30 -76 -196 -512 -1353 -3610 -9713 -26324 -71799 -196938 -542895 -1503312 -4179603 |
| Alt | DiagCol2T(n + 2, 2) | A005322 | 1 3 9 25 69 189 518 1422 3915 10813 29964 83304 232323 649845 1822824 5126520 14453451 40843521 |
| Alt | DiagCol3T(n + 3, 3) | A005323 | -1 -4 -14 -44 -133 -392 -1140 -3288 -9438 -27016 -77220 -220584 -630084 -1800384 -5147328 -14727168 |
| Alt | Polysee docs | missing | 1 1 1 2 0 1 4 1 -1 1 9 1 2 -2 1 21 3 -2 5 -3 1 51 6 5 -11 10 -4 1 127 15 -3 27 -32 17 -5 1 323 36 |
| 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 | A002522 | 2 1 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | A094792 | 4 1 -2 -11 -32 -71 -134 -227 -356 -527 -746 -1019 -1352 -1751 -2222 -2771 -3404 -4127 -4946 -5867 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A344507 | 1 -1 2 -2 5 -3 15 3 59 73 308 632 1951 4829 13674 36306 100827 275493 765150 2120466 5918943 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 5 -11 27 -60 147 -326 803 -1766 4399 -9535 24181 -51252 133533 -273699 742155 -1447206 4162407 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 2 -11 105 -1254 18495 -323322 6537923 -150081824 3855219588 -109554218575 3412072766311 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A026300 | 1 1 1 1 2 2 1 3 5 4 1 4 9 12 9 1 5 14 25 30 21 1 6 20 44 69 76 51 1 7 27 70 133 189 196 127 1 8 35 |
| Rev | Accsee docs | missing | 1 1 2 1 3 5 1 4 9 13 1 5 14 26 35 1 6 20 45 75 96 1 7 27 71 140 216 267 1 8 35 105 238 427 623 750 |
| Rev | AccRevsee docs | missing | 1 1 2 2 4 5 4 9 12 13 9 21 30 34 35 21 51 76 90 95 96 51 127 196 240 260 266 267 127 323 512 645 |
| Rev | AntiDiagsee docs | missing | 1 1 1 1 1 2 1 3 2 1 4 5 1 5 9 4 1 6 14 12 1 7 20 25 9 1 8 27 44 30 1 9 35 70 69 21 1 10 44 104 133 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 4 6 1 6 15 16 1 8 27 48 45 1 10 42 100 150 126 1 12 60 176 345 456 357 1 14 81 280 665 1134 |
| Rev | RowSum∑ k=0..n T(n, k) | A005773 | 1 2 5 13 35 96 267 750 2123 6046 17303 49721 143365 414584 1201917 3492117 10165779 29643870 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 3 6 19 45 141 357 1107 2907 8953 24068 73789 201643 616227 1704510 5196627 14508939 44152809 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 2 7 16 51 126 393 1016 3139 8350 25653 69576 212941 585690 1787607 4969152 15134931 42422022 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A005043 | 1 0 1 -1 3 -6 15 -36 91 -232 603 -1585 4213 -11298 30537 -83097 227475 -625992 1730787 -4805595 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A005773 | 1 2 5 13 35 96 267 750 2123 6046 17303 49721 143365 414584 1201917 3492117 10165779 29643870 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A191519 | 1 1 2 3 6 10 19 33 62 110 205 368 683 1235 2286 4153 7674 13986 25813 47150 86949 159077 293176 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A000244 | 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A026943 | 1 3 11 38 129 429 1407 4563 14669 46823 148587 469226 1475669 4624437 14447703 45017082 139937301 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 60 36 1050 4903140 63847980 448240898560 10968190265340 203258629623949200 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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) | | A026938 | 1 1 2 5 12 30 76 196 518 1422 3915 10813 29964 83304 232323 649845 1822824 5147328 14727168 |
| Rev | ColMiddleT(n, n // 2) | A026307 | 1 1 2 3 9 14 44 70 230 369 1242 2002 6853 11076 38376 62127 217242 352070 1239980 2010998 7123765 |
| Rev | CentralET(2 n, n) | A026302 | 1 2 9 44 230 1242 6853 38376 217242 1239980 7123765 41141916 238637282 1389206210 8112107475 |
| Rev | CentralOT(2 n + 1, n) | A327871 | 1 3 14 70 369 2002 11076 62127 352070 2010998 11559030 66780155 387444085 2255875650 13174629240 |
| 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) | A001006 | 1 1 2 4 9 21 51 127 323 835 2188 5798 15511 41835 113634 310572 853467 2356779 6536382 18199284 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | A344502 | 1 2 7 29 128 587 2759 13190 63844 311948 1535488 7602971 37829455 188989166 947399951 4763280965 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A344503 | 1 0 -1 -3 0 5 15 0 -28 -84 0 165 495 0 -1001 -3003 0 6188 18564 0 -38760 -116280 0 245157 735471 0 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 6 25 94 333 1140 3813 12546 40777 131284 419505 1332304 4209853 13245786 41524965 129771522 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A026943 | 1 3 11 38 129 429 1407 4563 14669 46823 148587 469226 1475669 4624437 14447703 45017082 139937301 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 10 59 292 1291 5322 20877 78972 290507 1045378 3695281 12871616 44285341 150775186 508719555 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A059738 | 1 3 10 34 117 405 1407 4899 17083 59629 208284 727900 2544751 8898873 31125138 108881166 380928795 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A344507 | 1 -1 2 -2 5 -3 15 3 59 73 308 632 1951 4829 13674 36306 100827 275493 765150 2120466 5918943 |
| Rev | DiagRow1T(n + 1, n) | A002026 | 1 2 5 12 30 76 196 512 1353 3610 9713 26324 71799 196938 542895 1503312 4179603 11662902 32652735 |
| Rev | DiagRow2T(n + 2, n) | A005322 | 1 3 9 25 69 189 518 1422 3915 10813 29964 83304 232323 649845 1822824 5126520 14453451 40843521 |
| Rev | DiagRow3T(n + 3, n) | A005323 | 1 4 14 44 133 392 1140 3288 9438 27016 77220 220584 630084 1800384 5147328 14727168 42171849 |
| Rev | DiagCol1T(n + 1, 1) | 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 | DiagCol2T(n + 2, 2) | A000096 | 2 5 9 14 20 27 35 44 54 65 77 90 104 119 135 152 170 189 209 230 252 275 299 324 350 377 405 434 |
| Rev | DiagCol3T(n + 3, 3) | A000297 | 4 12 25 44 70 104 147 200 264 340 429 532 650 784 935 1104 1292 1500 1729 1980 2254 2552 2875 3224 |
| Rev | Polysee docs | missing | 1 1 1 1 2 1 1 5 3 1 1 13 13 4 1 1 35 59 25 5 1 1 96 285 163 41 6 1 1 267 1419 1147 349 61 7 1 1 750 |
| 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 | A001844 | 1 5 13 25 41 61 85 113 145 181 221 265 313 365 421 481 545 613 685 761 841 925 1013 1105 1201 1301 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 13 59 163 349 641 1063 1639 2393 3349 4531 5963 7669 9673 11999 14671 17713 21149 25003 29299 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A330799 | 1 3 13 59 285 1419 7245 37659 198589 1059371 5705517 30976571 169338781 931239243 5147825421 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 4 25 163 1147 8350 62623 479488 3733603 29464012 235114411 1893694435 15374142901 125675225554 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 13 163 3233 87876 3070117 131170404 6642415873 389190947878 25916745005501 1933826196058571 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A026300 | 1 1 1 1 2 2 1 3 5 4 1 4 9 12 9 1 5 14 25 30 21 1 6 20 44 69 76 51 1 7 27 70 133 189 196 127 1 8 35 |
| Inv | Accsee docs | missing | 1 -1 0 0 -2 -1 1 2 -1 0 -1 1 4 0 1 0 -4 -2 4 -1 0 1 3 -6 -6 4 -2 -1 -1 2 11 -4 -9 6 -1 0 0 -6 -3 21 |
| Inv | AccRevsee docs | missing | 1 1 0 1 -1 -1 1 -2 -1 0 1 -3 0 2 1 1 -4 2 4 0 0 1 -5 5 5 -4 -2 -1 1 -6 9 4 -11 -2 1 0 1 -7 14 0 -20 |
| Inv | AntiDiagsee docs | A249303 | 1 -1 0 1 1 -2 -1 1 1 0 2 -3 1 -4 3 1 -1 2 2 -4 0 3 -9 6 1 1 -6 9 0 -5 -1 3 3 -15 10 1 0 4 -18 24 -5 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 0 -4 3 1 2 -9 4 -1 4 9 -16 5 0 -8 6 24 -25 6 1 4 -27 0 50 -36 7 -1 6 27 -60 -25 90 -49 8 0 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | A004525 | 1 -1 1 -2 3 -3 3 -4 5 -5 5 -6 7 -7 7 -8 9 -9 9 -10 11 -11 11 -12 13 -13 13 -14 15 -15 15 -16 17 -17 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | A004524 | 0 1 -2 2 -2 3 -4 4 -4 5 -6 6 -6 7 -8 8 -8 9 -10 10 -10 11 -12 12 -12 13 -14 14 -14 15 -16 16 -16 17 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^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 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 2 3 6 11 18 29 56 97 164 287 484 837 1474 2633 4362 7453 12776 22917 39364 69701 117636 198631 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A026741 | 1 -1 -3 2 5 -3 -7 4 9 -5 -11 6 13 -7 -15 8 17 -9 -19 10 21 -11 -23 12 25 -13 -27 14 29 -15 -31 16 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A057979 | 1 1 -1 -2 1 3 -1 -4 1 5 -1 -6 1 7 -1 -8 1 9 -1 -10 1 11 -1 -12 1 13 -1 -14 1 15 -1 -16 1 17 -1 -18 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 3 12 60 90 315 840 1764 5040 970200 803880 4110986880 85790905200 1693106415 1163962800 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A132199 | 1 1 2 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 3 4 6 10 15 24 49 84 126 210 384 627 935 1672 2860 4290 8151 15015 24804 37128 64974 117572 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -2 1 3 2 0 -15 -20 49 84 -98 -210 48 264 561 495 -2860 -4290 8151 15015 -12948 -31824 -9282 |
| Inv | CentralET(2 n, n) | missing | 1 -2 3 0 -20 84 -210 264 495 -4290 15015 -31824 18564 180880 -969000 2852736 -4724844 -2753100 |
| Inv | CentralOT(2 n + 1, n) | A350383 | -1 1 2 -15 49 -98 48 561 -2860 8151 -12948 -9282 149226 -594320 1428952 -1448655 -5538975 37450900 |
| 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 -3 -4 10 36 -7 -224 -279 980 3168 -1572 -22490 -22932 111465 313328 -263534 -2441556 -1890937 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 5 12 26 46 41 -152 -1175 -5208 -18888 -60444 -174186 -449122 -995255 -1642192 -437358 12193982 |
| Inv | TransNat0∑ k=0..n T(n, k) k | A142150 | 0 1 0 -2 0 3 0 -4 0 5 0 -6 0 7 0 -8 0 9 0 -10 0 11 0 -12 0 13 0 -14 0 15 0 -16 0 17 0 -18 0 19 0 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | A057979 | 1 1 -1 -2 1 3 -1 -4 1 5 -1 -6 1 7 -1 -8 1 9 -1 -10 1 11 -1 -12 1 13 -1 -14 1 15 -1 -16 1 17 -1 -18 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | A129889 | 0 1 2 -2 -6 3 12 -4 -20 5 30 -6 -42 7 56 -8 -72 9 90 -10 -110 11 132 -12 -156 13 182 -14 -210 15 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A106853 | 1 -1 -3 7 5 -33 13 119 -171 -305 989 231 -4187 3263 13485 -26537 -27403 133551 -23939 -510265 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A049072 | 1 3 5 3 -11 -45 -91 -93 85 627 1541 2115 181 -7917 -24475 -41757 -27371 84915 364229 753027 802165 |
| Inv | DiagRow1T(n + 1, 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 |
| Inv | DiagRow2T(n + 2, n) | A000217 | 0 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 |
| Inv | DiagRow3T(n + 3, n) | A005586 | 1 2 2 0 -5 -14 -28 -48 -75 -110 -154 -208 -273 -350 -440 -544 -663 -798 -950 -1120 -1309 -1518 |
| Inv | DiagCol2T(n + 2, 2) | A128504 | 1 -3 3 2 -9 9 3 -18 18 4 -30 30 5 -45 45 6 -63 63 7 -84 84 8 -108 108 9 -135 135 10 -165 165 11 |
| Inv | DiagCol3T(n + 3, 3) | missing | 1 -4 6 0 -15 24 -6 -36 60 -20 -70 120 -45 -120 210 -84 -189 336 -140 -280 504 -216 -396 720 -315 |
| Inv | Polysee docs | missing | 1 -1 1 0 0 1 1 -1 1 1 -1 0 0 2 1 0 1 -1 3 3 1 1 0 -1 4 8 4 1 -1 -1 0 5 21 15 5 1 0 0 1 6 55 56 24 6 |
| 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 | A005563 | 0 -1 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | A242135 | 1 0 -1 4 21 56 115 204 329 496 711 980 1309 1704 2171 2716 3345 4064 4879 5796 6821 7960 9219 10604 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^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 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 0 4 55 780 12649 235416 4976784 118118440 3114015839 90354434940 2862615066961 98356624289364 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A064189 | 1 1 1 2 2 1 4 5 3 1 9 12 9 4 1 21 30 25 14 5 1 51 76 69 44 20 6 1 127 196 189 133 70 27 7 1 323 512 |
| Inv:Rev | Accsee docs | missing | 1 1 0 1 -1 -1 1 -2 -1 0 1 -3 0 2 1 1 -4 2 4 0 0 1 -5 5 5 -4 -2 -1 1 -6 9 4 -11 -2 1 0 1 -7 14 0 -20 |
| Inv:Rev | AccRevsee docs | missing | 1 -1 0 0 -2 -1 1 2 -1 0 -1 1 4 0 1 0 -4 -2 4 -1 0 1 3 -6 -6 4 -2 -1 -1 2 11 -4 -9 6 -1 0 0 -6 -3 21 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 -1 1 -2 1 -3 0 1 -4 1 1 -5 3 1 1 -6 6 2 1 -7 10 2 -1 1 -8 15 0 -4 1 -9 21 -5 -9 0 1 -10 28 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -4 0 1 -6 3 4 1 -8 9 8 -5 1 -10 18 8 -20 0 1 -12 30 0 -45 12 7 1 -14 45 -20 -75 54 21 -8 1 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | A004525 | 1 1 1 2 3 3 3 4 5 5 5 6 7 7 7 8 9 9 9 10 11 11 11 12 13 13 13 14 15 15 15 16 17 17 17 18 19 19 19 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | A004524 | 0 -1 -2 -2 -2 -3 -4 -4 -4 -5 -6 -6 -6 -7 -8 -8 -8 -9 -10 -10 -10 -11 -12 -12 -12 -13 -14 -14 -14 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^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 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | missing | 1 2 3 6 11 18 29 56 97 164 287 484 837 1474 2633 4362 7453 12776 22917 39364 69701 117636 198631 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -1 -2 -2 0 3 5 4 -1 -8 -12 -8 5 21 28 15 -18 -54 -64 -25 57 136 143 32 -168 -336 -311 -7 472 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A057979 | 1 1 -1 -2 1 3 -1 -4 1 5 -1 -6 1 7 -1 -8 1 9 -1 -10 1 11 -1 -12 1 13 -1 -14 1 15 -1 -16 1 17 -1 -18 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A026741 | 1 -1 -3 2 5 -3 -7 4 9 -5 -11 6 13 -7 -15 8 17 -9 -19 10 21 -11 -23 12 25 -13 -27 14 29 -15 -31 16 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 3 12 60 90 315 840 1764 5040 970200 803880 4110986880 85790905200 1693106415 1163962800 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A132199 | 1 1 2 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 3 4 6 10 15 24 49 84 126 210 384 627 935 1672 2860 4290 8151 15015 24804 37128 64974 117572 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -2 -3 3 6 0 -5 -20 -21 84 126 -210 -384 264 693 495 0 -4290 -5577 15015 24804 -31824 -64974 |
| Inv:Rev | CentralET(2 n, n) | missing | 1 -2 3 0 -20 84 -210 264 495 -4290 15015 -31824 18564 180880 -969000 2852736 -4724844 -2753100 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -3 6 -5 -21 126 -384 693 0 -5577 24804 -64974 85918 155040 -1418616 5103723 -11110725 7079400 |
| 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 -3 -4 10 36 -7 -224 -279 980 3168 -1572 -22490 -22932 111465 313328 -263534 -2441556 -1890937 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 5 -12 26 -46 41 152 -1175 5208 -18888 60444 -174186 449122 -995255 1642192 -437358 -12193982 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | A029578 | 0 -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 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A026741 | 1 -1 -3 2 5 -3 -7 4 9 -5 -11 6 13 -7 -15 8 17 -9 -19 10 21 -11 -23 12 25 -13 -27 14 29 -15 -31 16 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 -2 10 10 -27 -24 52 44 -85 -70 126 102 -175 -140 232 184 -297 -234 370 290 -451 -352 540 420 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A001906 | 1 -3 8 -21 55 -144 377 -987 2584 -6765 17711 -46368 121393 -317811 832040 -2178309 5702887 |
| Inv:Rev | DiagRow2T(n + 2, n) | A128504 | 1 -3 3 2 -9 9 3 -18 18 4 -30 30 5 -45 45 6 -63 63 7 -84 84 8 -108 108 9 -135 135 10 -165 165 11 |
| Inv:Rev | DiagRow3T(n + 3, n) | missing | 1 -4 6 0 -15 24 -6 -36 60 -20 -70 120 -45 -120 210 -84 -189 336 -140 -280 504 -216 -396 720 -315 |
| Inv:Rev | DiagCol1T(n + 1, 1) | 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 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A000217 | 0 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 |
| Inv:Rev | DiagCol3T(n + 3, 3) | A005586 | 1 2 2 0 -5 -14 -28 -48 -75 -110 -154 -208 -273 -350 -440 -544 -663 -798 -950 -1120 -1309 -1518 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 0 1 1 -1 -1 1 1 0 -3 -2 1 1 1 7 -5 -3 1 1 0 5 28 -7 -4 1 1 -1 -33 -11 69 -9 -5 1 1 0 13 |
| 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 | 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 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 0 7 28 69 136 235 372 553 784 1071 1420 1837 2328 2899 3556 4305 5152 6103 7164 8341 9640 11067 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A106853 | 1 -1 -3 7 5 -33 13 119 -171 -305 989 231 -4187 3263 13485 -26537 -27403 133551 -23939 -510265 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A025170 | 1 -2 -5 28 -11 -230 559 952 -6935 5302 51811 -151340 -163619 1689298 -1906025 -11391632 39937489 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -3 28 -95 -2124 50869 -356376 -11097855 430015960 -4586784499 -186333758940 9987890296033 |
| << | 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.