OEIS Similars: A374440
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A374440 | 1 1 0 1 1 1 1 2 1 0 1 3 1 1 1 1 4 1 3 2 0 1 5 1 6 3 1 1 1 6 1 10 4 4 3 0 1 7 1 15 5 10 6 1 1 1 8 1 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 0 1 1 1 1 0 1 2 1 1 1 1 3 1 0 2 3 1 4 1 1 1 3 6 1 5 1 0 3 4 4 10 1 6 1 1 1 6 10 5 15 1 7 1 0 4 5 |
| Std | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 0 1 -1 -1 1 2 1 -2 1 -6 -3 5 -3 1 25 12 -21 11 -4 1 -129 -61 109 -58 19 -5 1 805 381 -679 363 |
| Std | Accsee docs | missing | 1 1 1 1 2 3 1 3 4 4 1 4 5 6 7 1 5 6 9 11 11 1 6 7 13 16 17 18 1 7 8 18 22 26 29 29 1 8 9 24 29 39 |
| Std | AccRevsee docs | missing | 1 0 1 1 2 3 0 1 3 4 1 2 3 6 7 0 2 5 6 10 11 1 2 5 11 12 17 18 0 3 7 11 21 22 28 29 1 2 8 18 23 38 |
| Std | AntiDiagsee docs | missing | 1 1 1 0 1 1 1 2 1 1 3 1 1 4 1 0 1 5 1 1 1 6 1 3 1 1 7 1 6 2 1 8 1 10 3 0 1 9 1 15 4 1 1 10 1 21 5 4 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 2 3 1 4 3 0 1 6 3 4 5 1 8 3 12 10 0 1 10 3 24 15 6 7 1 12 3 40 20 24 21 0 1 14 3 60 25 60 |
| Std | RowSum∑ k=0..n T(n, k) | A000032 | 1 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603 64079 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A001611 | 1 1 2 2 3 4 6 9 14 22 35 56 90 145 234 378 611 988 1598 2585 4182 6766 10947 17712 28658 46369 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A000071 | 0 0 1 2 4 7 12 20 33 54 88 143 232 376 609 986 1596 2583 4180 6764 10945 17710 28656 46367 75024 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A001911 | 1 1 1 0 -1 -3 -6 -11 -19 -32 -53 -87 -142 -231 -375 -608 -985 -1595 -2582 -4179 -6763 -10944 -17709 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000032 | 1 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603 64079 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 2 4 5 6 8 12 17 23 31 43 60 83 114 157 217 300 414 571 788 1088 1502 2073 2861 3949 5451 7524 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 6 12 23 43 78 140 248 436 761 1321 2282 3926 6730 11500 19595 33303 56470 95552 161372 272052 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 6 8 19 34 66 121 222 400 715 1266 2226 3889 6758 11688 20131 34546 59090 100777 171422 290896 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | A025560 | 1 1 1 2 3 12 30 60 210 840 1260 2520 13860 27720 180180 360360 180180 720720 6126120 12252240 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A167155 | 1 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 |
| Std | RowMaxMax k=0..n | T(n, k) | | A073028 | 1 1 1 2 3 4 6 10 15 21 35 56 84 126 210 330 495 792 1287 2002 3003 5005 8008 12376 19448 31824 |
| Std | ColMiddleT(n, n // 2) | missing | 1 1 1 2 1 1 6 10 5 6 35 56 28 36 210 330 165 220 1287 2002 1001 1365 8008 12376 6188 8568 50388 |
| Std | CentralET(2 n, n) | missing | 1 1 1 6 5 35 28 210 165 1287 1001 8008 6188 50388 38760 319770 245157 2042975 1562275 13123110 |
| Std | CentralOT(2 n + 1, n) | missing | 1 2 1 10 6 56 36 330 220 2002 1365 12376 8568 77520 54264 490314 346104 3124550 2220075 20030010 |
| 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) | A000035 | 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 |
| Std | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 4 10 24 71 218 659 2012 6205 19197 59555 185342 578293 1808186 5664594 17776204 55868937 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 0 2 -8 29 -94 293 -916 2867 -8963 28049 -87922 275963 -867242 2728746 -8595764 27106023 |
| Std | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 3 4 12 23 48 92 175 324 592 1067 1904 3368 5915 10324 17924 30975 53312 91428 156295 266420 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 6 8 19 34 66 121 222 400 715 1266 2226 3889 6758 11688 20131 34546 59090 100777 171422 290896 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 5 6 32 67 172 372 805 1658 3348 6603 12808 24472 46181 86206 159416 292371 532308 962860 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 2 7 18 47 120 303 758 1883 4652 11443 28050 68567 167232 407127 989678 2402867 5828180 14124763 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 3 -2 -5 32 -117 362 -1033 2812 -7425 19198 -48893 123128 -307437 762578 -1881745 4624372 |
| Std | DiagRow1T(n + 1, n) | A057979 | 1 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 1 19 1 20 1 21 1 |
| Std | DiagRow2T(n + 2, n) | missing | 1 2 1 3 3 4 6 5 10 6 15 7 21 8 28 9 36 10 45 11 55 12 66 13 78 14 91 15 105 16 120 17 136 18 153 19 |
| Std | DiagRow3T(n + 3, n) | missing | 1 3 1 6 4 10 10 15 20 21 35 28 56 36 84 45 120 55 165 66 220 78 286 91 364 105 455 120 560 136 680 |
| Std | DiagCol1T(n + 1, 1) | 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 | DiagCol2T(n + 2, 2) | 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 | DiagCol3T(n + 3, 3) | 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 |
| Std | Polysee docs | missing | 1 1 1 1 1 1 1 3 1 1 1 4 7 1 1 1 7 9 13 1 1 1 11 35 16 21 1 1 1 18 69 127 25 31 1 1 1 29 207 265 349 |
| Std | PolyRow1∑ k=0..1 T(1, k) n^k | 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 | PolyRow2∑ k=0..2 T(2, k) n^k | A002061 | 1 3 7 13 21 31 43 57 73 91 111 133 157 183 211 241 273 307 343 381 421 463 507 553 601 651 703 757 |
| Std | PolyRow3∑ k=0..3 T(3, 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 | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 7 9 35 69 207 481 1307 3229 8455 21369 55187 140661 361407 924049 2369675 6065869 15544567 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 13 16 127 265 1402 3781 16393 50416 197947 651685 2433202 8298361 30197173 104882416 376656967 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 7 16 349 1671 59683 433301 20803193 202651948 12168598191 148850424669 10713887029717 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A374440 | 1 1 0 1 -1 1 1 -2 1 0 1 -3 1 -1 1 1 -4 1 -3 2 0 1 -5 1 -6 3 -1 1 1 -6 1 -10 4 -4 3 0 1 -7 1 -15 5 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 0 1 1 -1 1 0 1 -2 1 1 -1 1 -3 1 0 2 -3 1 -4 1 1 -1 3 -6 1 -5 1 0 3 -4 4 -10 1 -6 1 1 -1 6 -10 5 |
| Alt | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 0 1 -1 1 1 -2 1 2 1 -6 3 5 3 1 -25 12 21 11 4 1 -129 61 109 58 19 5 1 -805 381 679 363 120 29 6 1 |
| Alt | Accsee docs | missing | 1 1 1 1 0 1 1 -1 0 0 1 -2 -1 -2 -1 1 -3 -2 -5 -3 -3 1 -4 -3 -9 -6 -7 -6 1 -5 -4 -14 -10 -14 -11 -11 |
| Alt | AccRevsee docs | missing | 1 0 1 1 0 1 0 1 -1 0 1 0 1 -2 -1 0 2 -1 0 -4 -3 1 0 3 -3 -2 -7 -6 0 3 -1 3 -7 -6 -12 -11 1 0 6 -4 1 |
| Alt | AntiDiagsee docs | missing | 1 1 1 0 1 -1 1 -2 1 1 -3 1 1 -4 1 0 1 -5 1 -1 1 -6 1 -3 1 1 -7 1 -6 2 1 -8 1 -10 3 0 1 -9 1 -15 4 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 -2 3 1 -4 3 0 1 -6 3 -4 5 1 -8 3 -12 10 0 1 -10 3 -24 15 -6 7 1 -12 3 -40 20 -24 21 0 1 -14 |
| Alt | RowSum∑ k=0..n T(n, k) | A001911 | 1 1 1 0 -1 -3 -6 -11 -19 -32 -53 -87 -142 -231 -375 -608 -985 -1595 -2582 -4179 -6763 -10944 -17709 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A001611 | 1 1 2 2 3 4 6 9 14 22 35 56 90 145 234 378 611 988 1598 2585 4182 6766 10947 17712 28658 46369 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A000071 | 0 0 -1 -2 -4 -7 -12 -20 -33 -54 -88 -143 -232 -376 -609 -986 -1596 -2583 -4180 -6764 -10945 -17710 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000032 | 1 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603 64079 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000032 | 1 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603 64079 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 0 0 -1 -2 -4 -6 -9 -13 -19 -27 -38 -53 -74 -103 -143 -198 -274 -379 -524 -724 -1000 -1381 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 2 0 -5 -15 -34 -68 -128 -232 -411 -717 -1238 -2122 -3618 -6144 -10401 -17563 -29594 -49776 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 2 0 -1 -6 -14 -31 -62 -120 -225 -414 -750 -1343 -2382 -4192 -7329 -12742 -22046 -37983 -65198 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | A025560 | 1 1 1 2 3 12 30 60 210 840 1260 2520 13860 27720 180180 360360 180180 720720 6126120 12252240 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A167155 | 1 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 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A073028 | 1 1 1 2 3 4 6 10 15 21 35 56 84 126 210 330 495 792 1287 2002 3003 5005 8008 12376 19448 31824 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 1 -1 -2 1 1 -6 -10 5 6 -35 -56 28 36 -210 -330 165 220 -1287 -2002 1001 1365 -8008 -12376 6188 |
| Alt | CentralET(2 n, n) | missing | 1 -1 1 -6 5 -35 28 -210 165 -1287 1001 -8008 6188 -50388 38760 -319770 245157 -2042975 1562275 |
| Alt | CentralOT(2 n + 1, n) | missing | 1 -2 1 -10 6 -56 36 -330 220 -2002 1365 -12376 8568 -77520 54264 -490314 346104 -3124550 2220075 |
| 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) | A000035 | 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 0 -2 -8 -29 -94 -293 -916 -2867 -8963 -28049 -87922 -275963 -867242 -2728746 -8595764 -27106023 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 4 -10 24 -71 218 -659 2012 -6205 19197 -59555 185342 -578293 1808186 -5664594 17776204 |
| Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 1 0 0 -3 -8 -20 -43 -88 -172 -327 -608 -1112 -2007 -3584 -6344 -11147 -19464 -33804 -58435 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 2 0 -1 -6 -14 -31 -62 -120 -225 -414 -750 -1343 -2382 -4192 -7329 -12742 -22046 -37983 -65198 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 3 2 8 5 4 -20 -77 -226 -556 -1267 -2728 -5656 -11389 -22422 -43344 -82539 -155204 -288716 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 2 3 2 -5 -32 -117 -362 -1033 -2812 -7425 -19198 -48893 -123128 -307437 -762578 -1881745 -4624372 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 7 -18 47 -120 303 -758 1883 -4652 11443 -28050 68567 -167232 407127 -989678 2402867 -5828180 |
| Alt | DiagRow1T(n + 1, n) | A057979 | 1 -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 |
| Alt | DiagRow2T(n + 2, n) | missing | 1 -2 1 -3 3 -4 6 -5 10 -6 15 -7 21 -8 28 -9 36 -10 45 -11 55 -12 66 -13 78 -14 91 -15 105 -16 120 |
| Alt | DiagRow3T(n + 3, n) | missing | 1 -3 1 -6 4 -10 10 -15 20 -21 35 -28 56 -36 84 -45 120 -55 165 -66 220 -78 286 -91 364 -105 455 |
| Alt | DiagCol1T(n + 1, 1) | 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 | DiagCol2T(n + 2, 2) | 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 | DiagCol3T(n + 3, 3) | A000217 | 0 -1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253 |
| Alt | Polysee docs | missing | 1 1 1 1 1 1 1 1 1 1 1 0 3 1 1 1 -1 1 7 1 1 1 -3 7 4 13 1 1 1 -6 5 55 9 21 1 1 1 -11 27 79 197 16 31 |
| Alt | PolyRow1∑ k=0..1 T(1, k) n^k | 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 | PolyRow2∑ k=0..2 T(2, k) n^k | A002061 | 1 1 3 7 13 21 31 43 57 73 91 111 133 157 183 211 241 273 307 343 381 421 463 507 553 601 651 703 |
| Alt | PolyRow3∑ k=0..3 T(3, 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 | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 3 1 7 5 27 41 143 301 867 2065 5527 13781 35883 91001 234527 598525 1536627 3930721 10077223 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 7 4 55 79 562 1261 6307 17644 74395 233179 902722 3001321 11125807 38137684 138269935 481509079 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 3 4 197 881 41479 291901 15938057 152429536 9861542011 119172816643 9006101100877 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 0 1 1 1 1 0 1 2 1 1 1 1 3 1 0 2 3 1 4 1 1 1 3 6 1 5 1 0 3 4 4 10 1 6 1 1 1 6 10 5 15 1 7 1 0 4 5 |
| Rev | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 -1 -1 1 2 1 -2 1 -6 -3 5 -3 1 25 12 -21 11 -4 1 -129 -61 109 -58 19 -5 1 805 381 -679 363 |
| Rev | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -1 -1 1 -2 1 2 1 -3 5 -3 -6 1 -4 11 -21 12 25 1 -5 19 -58 109 -61 -129 1 -6 29 -120 363 |
| Rev | Accsee docs | missing | 1 0 1 1 2 3 0 1 3 4 1 2 3 6 7 0 2 5 6 10 11 1 2 5 11 12 17 18 0 3 7 11 21 22 28 29 1 2 8 18 23 38 |
| Rev | AccRevsee docs | missing | 1 1 1 1 2 3 1 3 4 4 1 4 5 6 7 1 5 6 9 11 11 1 6 7 13 16 17 18 1 7 8 18 22 26 29 29 1 8 9 24 29 39 |
| Rev | AntiDiagsee docs | missing | 1 0 1 1 0 1 1 1 1 0 1 2 1 2 1 1 0 1 3 3 1 3 3 1 1 0 1 4 6 4 1 4 6 4 1 1 0 1 5 10 10 5 1 5 10 10 5 1 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 0 2 1 2 3 0 2 6 4 1 2 3 12 5 0 4 9 4 20 6 1 2 9 24 5 30 7 0 6 12 16 50 6 42 8 1 2 18 40 25 90 7 |
| Rev | RowSum∑ k=0..n T(n, k) | A000032 | 1 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603 64079 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 0 2 2 3 7 6 20 14 54 35 143 90 376 234 986 611 2583 1598 6764 4182 17710 10947 46367 28658 121392 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 1 2 4 4 12 9 33 22 88 56 232 145 609 378 1596 988 4180 2585 10945 6766 28656 17712 75024 46369 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A001911 | 1 -1 1 0 -1 3 -6 11 -19 32 -53 87 -142 231 -375 608 -985 1595 -2582 4179 -6763 10944 -17709 28655 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000032 | 1 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349 15127 24476 39603 64079 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A086341 | 1 0 2 1 3 3 5 7 9 15 17 31 33 63 65 127 129 255 257 511 513 1023 1025 2047 2049 4095 4097 8191 8193 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 6 8 19 34 66 121 222 400 715 1266 2226 3889 6758 11688 20131 34546 59090 100777 171422 290896 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 6 12 23 43 78 140 248 436 761 1321 2282 3926 6730 11500 19595 33303 56470 95552 161372 272052 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | A025560 | 1 1 1 2 3 12 30 60 210 840 1260 2520 13860 27720 180180 360360 180180 720720 6126120 12252240 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A167155 | 1 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 |
| Rev | RowMaxMax k=0..n | T(n, k) | | A073028 | 1 1 1 2 3 4 6 10 15 21 35 56 84 126 210 330 495 792 1287 2002 3003 5005 8008 12376 19448 31824 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 0 1 1 1 3 6 4 5 20 35 21 28 126 210 120 165 792 1287 715 1001 5005 8008 4368 6188 31824 50388 |
| Rev | CentralET(2 n, n) | missing | 1 1 1 6 5 35 28 210 165 1287 1001 8008 6188 50388 38760 319770 245157 2042975 1562275 13123110 |
| Rev | CentralOT(2 n + 1, n) | missing | 0 1 3 4 20 21 126 120 792 715 5005 4368 31824 27132 203490 170544 1307504 1081575 8436285 6906900 |
| Rev | ColLeftT(n, 0) | A000035 | 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 |
| 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 1 4 10 24 71 218 659 2012 6205 19197 59555 185342 578293 1808186 5664594 17776204 55868937 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 0 -2 -8 -29 -94 -293 -916 -2867 -8963 -28049 -87922 -275963 -867242 -2728746 -8595764 -27106023 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 3 8 16 32 60 111 201 360 638 1122 1960 3405 5887 10136 17388 29732 50692 86203 146245 247576 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 6 12 23 43 78 140 248 436 761 1321 2282 3926 6730 11500 19595 33303 56470 95552 161372 272052 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 5 18 48 112 244 505 1013 1982 3808 7208 13480 24953 45789 83386 150840 271240 485148 863585 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 7 9 35 69 207 481 1307 3229 8455 21369 55187 140661 361407 924049 2369675 6065869 15544567 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 1 3 1 7 5 27 41 143 301 867 2065 5527 13781 35883 91001 234527 598525 1536627 3930721 10077223 |
| Rev | DiagRow1T(n + 1, n) | 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 |
| Rev | DiagRow2T(n + 2, 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 | DiagRow3T(n + 3, 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 |
| Rev | DiagCol1T(n + 1, 1) | A057979 | 1 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 1 19 1 20 1 21 1 |
| Rev | DiagCol2T(n + 2, 2) | missing | 1 2 1 3 3 4 6 5 10 6 15 7 21 8 28 9 36 10 45 11 55 12 66 13 78 14 91 15 105 16 120 17 136 18 153 19 |
| Rev | DiagCol3T(n + 3, 3) | missing | 1 3 1 6 4 10 10 15 20 21 35 28 56 36 84 45 120 55 165 66 220 78 286 91 364 105 455 120 560 136 680 |
| Rev | Polysee docs | missing | 1 0 1 1 1 1 0 3 2 1 1 4 7 3 1 0 7 18 13 4 1 1 11 47 48 21 5 1 0 18 120 175 100 31 6 1 1 29 303 627 |
| Rev | PolyRow1∑ k=0..1 T(1, 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 |
| Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A002061 | 1 3 7 13 21 31 43 57 73 91 111 133 157 183 211 241 273 307 343 381 421 463 507 553 601 651 703 757 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A045991 | 0 4 18 48 100 180 294 448 648 900 1210 1584 2028 2548 3150 3840 4624 5508 6498 7600 8820 10164 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 7 18 47 120 303 758 1883 4652 11443 28050 68567 167232 407127 989678 2402867 5828180 14124763 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 13 48 175 627 2218 7767 26977 93072 319315 1090383 3708562 12570363 42482533 143206608 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 7 48 469 5835 88243 1571843 32236937 748230732 19390666011 555019810719 17390281503037 |
| Rev:Inv | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 0 1 -1 -1 1 2 1 -2 1 -6 -3 5 -3 1 25 12 -21 11 -4 1 -129 -61 109 -58 19 -5 1 805 381 -679 363 |
| Rev:Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -1 -1 1 -2 1 2 1 -3 5 -3 -6 1 -4 11 -21 12 25 1 -5 19 -58 109 -61 -129 1 -6 29 -120 363 |
| Rev:Inv | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 1 1 1 0 1 2 1 1 1 1 3 1 0 2 3 1 4 1 1 1 3 6 1 5 1 0 3 4 4 10 1 6 1 1 1 6 10 5 15 1 7 1 0 4 5 |
| Rev:Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A374440 | 1 1 0 1 1 1 1 2 1 0 1 3 1 1 1 1 4 1 3 2 0 1 5 1 6 3 1 1 1 6 1 10 4 4 3 0 1 7 1 15 5 10 6 1 1 1 8 1 |
| Rev:Inv | Accsee docs | missing | 1 0 1 -1 -2 -1 2 3 1 2 -6 -9 -4 -7 -6 25 37 16 27 23 24 -129 -190 -81 -139 -120 -125 -124 805 1186 |
| Rev:Inv | AccRevsee docs | missing | 1 1 1 1 0 -1 1 -1 0 2 1 -2 3 0 -6 1 -3 8 -13 -1 24 1 -4 15 -43 66 5 -124 1 -5 24 -96 267 -412 -31 |
| Rev:Inv | AntiDiagsee docs | missing | 1 0 -1 1 2 -1 -6 1 1 25 -3 -2 -129 12 5 1 805 -61 -21 -3 -5866 381 109 11 1 48787 -2776 -679 -58 -4 |
| Rev:Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 -1 -2 3 2 2 -6 4 -6 -6 15 -12 5 25 24 -63 44 -20 6 -129 -122 327 -232 95 -30 7 805 762 -2037 |
| Rev:Inv | RowSum∑ k=0..n T(n, k) | missing | 1 1 -1 2 -6 24 -124 774 -5639 46900 -438036 4536884 -51590479 638835208 -8555522682 123203682122 |
| Rev:Inv | EvenSum∑ k=0..n T(n, k) even(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:Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -1 2 -6 24 -124 774 -5639 46900 -438036 4536884 -51590479 638835208 -8555522682 123203682122 |
| Rev:Inv | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 -1 1 -2 6 -24 124 -774 5639 -46900 438036 -4536884 51590479 -638835208 8555522682 -123203682122 |
| Rev:Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 1 3 6 18 74 382 2384 17371 144474 1349356 13975732 158922881 1967912178 26355024068 379525147442 |
| Rev:Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 0 1 -4 20 -111 720 -5364 45270 -427242 4459874 -51025613 634948648 -8537810795 123363709868 |
| Rev:Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -4 8 -32 152 -908 6444 -52586 484260 -4960926 55918834 -687462902 9151559168 -131116663714 |
| Rev:Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 0 2 -4 16 -84 522 -3804 31640 -295506 3060658 -34803804 430968952 -5771699198 83115271814 |
| Rev:Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 2 30 23100 4726042710 835152807720 5656703989612731384 141919725585103592780965871560 |
| Rev:Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A174965 | 1 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 |
| Rev:Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 2 6 25 129 805 5866 48787 455660 4719424 53666201 664538485 8899750693 128160732660 |
| Rev:Inv | ColMiddleT(n, n // 2) | missing | 1 0 -1 1 5 -21 -58 363 876 -7283 -16565 171571 377656 -4676446 -10085978 145242958 308979028 |
| Rev:Inv | CentralET(2 n, n) | missing | 1 -1 5 -58 876 -16565 377656 -10085978 308979028 -10683247217 411598827138 -17487475648780 |
| Rev:Inv | CentralOT(2 n + 1, n) | missing | 0 1 -21 363 -7283 171571 -4676446 145242958 -5071425129 196822555519 -8409534410222 392380624284412 |
| Rev:Inv | ColLeftT(n, 0) | missing | 1 0 -1 2 -6 25 -129 805 -5866 48787 -455660 4719424 -53666201 664538485 -8899750693 128160732660 |
| 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 -2 0 1 -34 236 -1714 12947 -99403 771226 -5713899 34611049 -28853252 -4898985378 140988839058 |
| Rev:Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 2 8 49 376 3348 33678 377347 4659123 62832666 918675027 14471158593 244269770850 4397792079758 |
| Rev:Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 1 0 2 -8 40 -252 1835 -15260 142530 -1476226 16786675 -207866256 2783823484 -40088410308 |
| Rev:Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 0 2 -4 16 -84 522 -3804 31640 -295506 3060658 -34803804 430968952 -5771699198 83115271814 |
| Rev:Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 3 2 6 -12 68 -430 3117 -25940 242276 -2509300 28534173 -353333276 4731972770 -68142706474 |
| Rev:Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 -5 17 -105 861 -8861 110649 -1612465 26821333 -501011973 10378296305 -236030387225 |
| Rev:Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 1 -1 -7 -45 -387 -4009 -50031 -729221 -12129755 -226578273 -4693496071 -106742729917 |
| Rev:Inv | DiagRow1T(n + 1, n) | 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 |
| Rev:Inv | DiagRow2T(n + 2, n) | A028387 | -1 1 5 11 19 29 41 55 71 89 109 131 155 181 209 239 271 305 341 379 419 461 505 551 599 649 701 755 |
| Rev:Inv | DiagRow3T(n + 3, n) | missing | 2 -3 -21 -58 -120 -213 -343 -516 -738 -1015 -1353 -1758 -2236 -2793 -3435 -4168 -4998 -5931 -6973 |
| Rev:Inv | DiagCol1T(n + 1, 1) | missing | 1 -1 1 -3 12 -61 381 -2776 23087 -215629 2233341 -25396091 314475028 -4211568491 60648631864 |
| Rev:Inv | DiagCol2T(n + 2, 2) | missing | 1 -2 5 -21 109 -679 4948 -41153 384358 -3980927 45268498 -560551300 7507114996 -108106102207 |
| Rev:Inv | DiagCol3T(n + 3, 3) | missing | 1 -3 11 -58 363 -2643 21983 -205317 2126533 -24181548 299435565 -4010154310 57748169854 |
| Rev:Inv | Polysee docs | missing | 1 0 1 -1 1 1 2 -1 2 1 -6 2 1 3 1 25 -6 4 5 4 1 -129 24 0 14 11 5 1 805 -124 21 30 38 19 6 1 -5866 |
| Rev:Inv | PolyRow1∑ k=0..1 T(1, 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 |
| Rev:Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A028387 | -1 -1 1 5 11 19 29 41 55 71 89 109 131 155 181 209 239 271 305 341 379 419 461 505 551 599 649 701 |
| Rev:Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 2 2 4 14 38 82 152 254 394 578 812 1102 1454 1874 2368 2942 3602 4354 5204 6158 7222 8402 9704 |
| Rev:Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 1 4 0 21 -71 507 -3586 30005 -279942 2899942 -32975447 408330053 -5468508411 78749180536 |
| Rev:Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 5 14 30 88 156 778 -685 19804 -145172 1615540 -18056645 224472328 -3003756406 43262425638 |
| Rev:Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 1 14 126 1560 23301 411642 8388950 193743700 5001236850 142694029924 4459262153923 |
| << | 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.