OEIS Similars: A371761, A272644
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A371761 | 1 0 0 0 1 0 0 1 1 0 0 1 5 1 0 0 1 13 13 1 0 0 1 29 73 29 1 0 0 1 61 301 301 61 1 0 0 1 125 1081 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A371761 | 1 0 0 0 1 0 0 1 1 0 0 1 5 1 0 0 1 13 13 1 0 0 1 29 73 29 1 0 0 1 61 301 301 61 1 0 0 1 125 1081 |
| Std | Accsee docs | missing | 1 0 0 0 1 1 0 1 2 2 0 1 6 7 7 0 1 14 27 28 28 0 1 30 103 132 133 133 0 1 62 363 664 725 726 726 0 1 |
| Std | AccRevsee docs | missing | 1 0 0 0 1 1 0 1 2 2 0 1 6 7 7 0 1 14 27 28 28 0 1 30 103 132 133 133 0 1 62 363 664 725 726 726 0 1 |
| Std | AntiDiagsee docs | missing | 1 0 0 0 0 1 0 1 0 0 1 1 0 1 5 0 0 1 13 1 0 1 29 13 0 0 1 61 73 1 0 1 125 301 29 0 0 1 253 1081 301 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 0 0 0 2 0 0 2 3 0 0 2 15 4 0 0 2 39 52 5 0 0 2 87 292 145 6 0 0 2 183 1204 1505 366 7 0 0 2 375 |
| Std | RowSum∑ k=0..n T(n, k) | A297195 | 1 0 1 2 7 28 133 726 4483 30896 235105 1957930 17712799 172980804 1813760317 20323234814 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 0 0 1 5 14 58 363 2319 15448 116516 978965 8875513 86490402 906415374 10161617407 121190933987 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 1 1 2 14 75 363 2164 15448 118589 978965 8837286 86490402 907344943 10161617407 121162113368 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A036968 | 1 0 -1 0 3 0 -17 0 155 0 -2073 0 38227 0 -929569 0 28820619 0 -1109652905 0 51943281731 0 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A297195 | 1 0 1 2 7 28 133 726 4483 30896 235105 1957930 17712799 172980804 1813760317 20323234814 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 0 1 1 2 6 15 43 136 456 1637 6253 25278 107802 483451 2273455 11182292 57397452 306813873 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 0 2 5 21 98 532 3267 22415 169928 1410630 12726545 123989593 1297356030 14510082536 172747495919 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 0 2 5 21 98 532 3267 22415 169928 1410630 12726545 123989593 1297356030 14510082536 172747495919 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 1 5 13 2117 18361 279573625 10586064709 32509554153536113 6696988536962584561 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 1 1 5 13 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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) | | A272645 | 1 0 1 1 5 13 73 301 2069 11581 95401 673261 6487445 55213453 610093513 6077248381 75796724309 |
| Std | ColMiddleT(n, n // 2) | A272645 | 1 0 1 1 5 13 73 301 2069 11581 95401 673261 6487445 55213453 610093513 6077248381 75796724309 |
| Std | CentralET(2 n, n) | A048144 | 1 1 5 73 2069 95401 6487445 610093513 75796724309 12020754177001 2369364111428885 |
| Std | CentralOT(2 n + 1, n) | missing | 0 1 13 301 11581 673261 55213453 6077248381 864806272861 154546274524621 33888536448984493 |
| Std | ColLeftT(n, 0) | 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 | ColRightT(n, n) | 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 | BinConv∑ k=0..n C(n, k) T(n, k) | A052841 | 1 0 2 6 38 270 2342 23646 272918 3543630 51123782 811316286 14045783798 263429174190 5320671485222 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A210657 | 1 0 -2 0 22 0 -602 0 30742 0 -2523002 0 303692662 0 -50402079002 0 11030684333782 0 |
| Std | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 1 3 14 70 399 2541 17932 139032 1175525 10768615 106276794 1124375226 12696322219 152424261105 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 0 2 5 21 98 532 3267 22415 169928 1410630 12726545 123989593 1297356030 14510082536 172747495919 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 1 5 30 186 1263 9331 74908 650880 6095061 61250545 657890826 7524868118 91341774379 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 0 2 6 30 174 1198 9486 84974 849678 9382254 113391246 1488810478 21103080462 321177039470 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 0 -2 2 10 -38 -38 762 -1766 -14086 122266 -29318 -5770982 36006906 148448410 -3757570438 |
| Std | DiagRow1T(n + 1, n) | A000012 | 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 | DiagRow2T(n + 2, n) | A036563 | 0 1 5 13 29 61 125 253 509 1021 2045 4093 8189 16381 32765 65533 131069 262141 524285 1048573 |
| Std | DiagRow3T(n + 3, n) | A006230 | 0 1 13 73 301 1081 3613 11593 36301 111961 342013 1038313 3139501 9467641 28501213 85700233 |
| Std | DiagCol1T(n + 1, 1) | A000012 | 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 | DiagCol2T(n + 2, 2) | A036563 | 0 1 5 13 29 61 125 253 509 1021 2045 4093 8189 16381 32765 65533 131069 262141 524285 1048573 |
| Std | DiagCol3T(n + 3, 3) | A006230 | 0 1 13 73 301 1081 3613 11593 36301 111961 342013 1038313 3139501 9467641 28501213 85700233 |
| Std | Polysee docs | missing | 1 0 1 0 0 1 0 1 0 1 0 2 2 0 1 0 7 6 3 0 1 0 28 30 12 4 0 1 0 133 174 75 20 5 0 1 0 726 1198 552 148 |
| Std | PolyRow2∑ k=0..2 T(2, k) n^k | A000027 | 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 35 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | A002378 | 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 756 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 0 2 6 30 174 1198 9486 84974 849678 9382254 113391246 1488810478 21103080462 321177039470 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 0 3 12 75 552 4827 48612 553899 7045824 98989851 1522413372 25439475243 458949619416 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 2 12 148 2580 62178 1971816 79323464 3935718000 235708233910 16749960290580 1392375762606108 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A371761 | 1 0 0 0 -1 0 0 -1 1 0 0 -1 5 -1 0 0 -1 13 -13 1 0 0 -1 29 -73 29 -1 0 0 -1 61 -301 301 -61 1 0 0 -1 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A371761 | 1 0 0 0 -1 0 0 1 -1 0 0 -1 5 -1 0 0 1 -13 13 -1 0 0 -1 29 -73 29 -1 0 0 1 -61 301 -301 61 -1 0 0 -1 |
| Alt | Accsee docs | missing | 1 0 0 0 -1 -1 0 -1 0 0 0 -1 4 3 3 0 -1 12 -1 0 0 0 -1 28 -45 -16 -17 -17 0 -1 60 -241 60 -1 0 0 0 |
| Alt | AccRevsee docs | missing | 1 0 0 0 -1 -1 0 1 0 0 0 -1 4 3 3 0 1 -12 1 0 0 0 -1 28 -45 -16 -17 -17 0 1 -60 241 -60 1 0 0 0 -1 |
| Alt | AntiDiagsee docs | missing | 1 0 0 0 0 -1 0 -1 0 0 -1 1 0 -1 5 0 0 -1 13 -1 0 -1 29 -13 0 0 -1 61 -73 1 0 -1 125 -301 29 0 0 -1 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 0 0 0 -2 0 0 -2 3 0 0 -2 15 -4 0 0 -2 39 -52 5 0 0 -2 87 -292 145 -6 0 0 -2 183 -1204 1505 -366 7 |
| Alt | RowSum∑ k=0..n T(n, k) | A036968 | 1 0 -1 0 3 0 -17 0 155 0 -2073 0 38227 0 -929569 0 28820619 0 -1109652905 0 51943281731 0 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 0 0 1 5 14 58 363 2319 15448 116516 978965 8875513 86490402 906415374 10161617407 121190933987 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 -1 -1 -2 -14 -75 -363 -2164 -15448 -118589 -978965 -8837286 -86490402 -907344943 -10161617407 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A297195 | 1 0 1 2 7 28 133 726 4483 30896 235105 1957930 17712799 172980804 1813760317 20323234814 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A297195 | 1 0 1 2 7 28 133 726 4483 30896 235105 1957930 17712799 172980804 1813760317 20323234814 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 0 -1 -1 0 4 11 15 -12 -148 -529 -1097 -72 12036 68723 242399 469116 -1007876 -15909577 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 0 -2 -1 9 10 -68 -123 775 2000 -12438 -42485 267589 1152150 -7436552 -38996527 259385571 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 0 -2 1 9 -10 -68 123 775 -2000 -12438 42485 267589 -1152150 -7436552 38996527 259385571 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 1 5 13 2117 18361 279573625 10586064709 32509554153536113 6696988536962584561 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 1 1 5 13 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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) | | A272645 | 1 0 1 1 5 13 73 301 2069 11581 95401 673261 6487445 55213453 610093513 6077248381 75796724309 |
| Alt | ColMiddleT(n, n // 2) | A272645 | 1 0 -1 -1 5 13 -73 -301 2069 11581 -95401 -673261 6487445 55213453 -610093513 -6077248381 |
| Alt | CentralET(2 n, n) | A048144 | 1 -1 5 -73 2069 -95401 6487445 -610093513 75796724309 -12020754177001 2369364111428885 |
| Alt | CentralOT(2 n + 1, n) | missing | 0 -1 13 -301 11581 -673261 55213453 -6077248381 864806272861 -154546274524621 33888536448984493 |
| Alt | ColLeftT(n, 0) | 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 | ColRightT(n, n) | 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 | BinConv∑ k=0..n C(n, k) T(n, k) | A210657 | 1 0 -2 0 22 0 -602 0 30742 0 -2523002 0 303692662 0 -50402079002 0 11030684333782 0 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A052841 | 1 0 2 -6 38 -270 2342 -23646 272918 -3543630 51123782 -811316286 14045783798 -263429174190 |
| Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 -1 1 6 -10 -51 123 620 -2000 -10365 42485 229362 -1152150 -6506983 38996527 230564952 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 0 -2 1 9 -10 -68 123 775 -2000 -12438 42485 267589 -1152150 -7436552 38996527 259385571 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -1 3 10 -50 -103 861 1300 -18000 -19941 467335 348814 -14977950 -5880627 584947905 19902776 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 0 -2 -2 10 38 -38 -762 -1766 14086 122266 29318 -5770982 -36006906 148448410 3757570438 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 0 2 -6 30 -174 1198 -9486 84974 -849678 9382254 -113391246 1488810478 -21103080462 321177039470 |
| Alt | DiagRow1T(n + 1, n) | A000012 | 0 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 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 | DiagRow2T(n + 2, n) | A036563 | 0 -1 5 -13 29 -61 125 -253 509 -1021 2045 -4093 8189 -16381 32765 -65533 131069 -262141 524285 |
| Alt | DiagRow3T(n + 3, n) | A006230 | 0 -1 13 -73 301 -1081 3613 -11593 36301 -111961 342013 -1038313 3139501 -9467641 28501213 -85700233 |
| Alt | DiagCol1T(n + 1, 1) | A000012 | 0 -1 -1 -1 -1 -1 -1 -1 -1 -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 | DiagCol2T(n + 2, 2) | A036563 | 0 1 5 13 29 61 125 253 509 1021 2045 4093 8189 16381 32765 65533 131069 262141 524285 1048573 |
| Alt | DiagCol3T(n + 3, 3) | A006230 | 0 -1 -13 -73 -301 -1081 -3613 -11593 -36301 -111961 -342013 -1038313 -3139501 -9467641 -28501213 |
| Alt | Polysee docs | missing | 1 0 1 0 0 1 0 -1 0 1 0 0 -2 0 1 0 3 2 -3 0 1 0 0 10 6 -4 0 1 0 -17 -38 15 12 -5 0 1 0 0 -38 -156 12 |
| Alt | PolyRow2∑ k=0..2 T(2, k) n^k | A000027 | 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 | PolyRow3∑ k=0..3 T(3, k) n^k | A002378 | 0 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 0 -2 2 10 -38 -38 762 -1766 -14086 122266 -29318 -5770982 36006906 148448410 -3757570438 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 0 -3 6 15 -156 393 2706 -34221 115728 1251789 -20842914 95148663 1254941052 -27304605615 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -2 6 12 -680 15078 -285138 3177784 142574976 -17255152110 1258102877350 -75274590564732 |
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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.