OEIS Similars: A072233, A008284, A058398
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A072233 | 1 0 1 0 1 1 0 1 1 1 0 1 2 1 1 0 1 2 2 1 1 0 1 3 3 2 1 1 0 1 3 4 3 2 1 1 0 1 4 5 5 3 2 1 1 0 1 4 7 6 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 1 1 0 1 1 2 1 0 1 1 2 2 1 0 1 1 2 3 3 1 0 1 1 2 3 4 3 1 0 1 1 2 3 5 5 4 1 0 1 1 2 3 5 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 -1 1 0 0 -1 1 0 1 -1 -1 1 0 0 1 -1 -1 1 0 0 1 0 -1 -1 1 0 -1 1 1 0 -1 -1 1 0 -1 0 2 0 0 -1 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -1 0 1 -1 0 0 1 -1 -1 1 0 1 -1 -1 1 0 0 1 -1 -1 0 1 0 0 1 -1 -1 0 1 1 -1 0 1 -1 -1 0 0 2 0 |
| Std | Accsee docs | missing | 1 0 1 0 1 2 0 1 2 3 0 1 3 4 5 0 1 3 5 6 7 0 1 4 7 9 10 11 0 1 4 8 11 13 14 15 0 1 5 10 15 18 20 21 |
| Std | AccRevsee docs | missing | 1 1 1 1 2 2 1 2 3 3 1 2 4 5 5 1 2 4 6 7 7 1 2 4 7 10 11 11 1 2 4 7 11 14 15 15 1 2 4 7 12 17 21 22 |
| Std | AntiDiagsee docs | missing | 1 0 0 1 0 1 0 1 1 0 1 1 0 1 2 1 0 1 2 1 0 1 3 2 1 0 1 3 3 1 0 1 4 4 2 1 0 1 4 5 3 1 0 1 5 7 5 2 1 0 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 2 3 0 2 3 4 0 2 6 4 5 0 2 6 8 5 6 0 2 9 12 10 6 7 0 2 9 16 15 12 7 8 0 2 12 20 25 18 14 8 9 |
| Std | RowSum∑ k=0..n T(n, k) | A000041 | 1 1 2 3 5 7 11 15 22 30 42 56 77 101 135 176 231 297 385 490 627 792 1002 1255 1575 1958 2436 3010 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A027187 | 1 0 1 1 3 3 6 7 12 14 22 27 40 49 69 86 118 146 195 242 317 392 505 623 793 973 1224 1498 1867 2274 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A027193 | 0 1 1 2 2 4 5 8 10 16 20 29 37 52 66 90 113 151 190 248 310 400 497 632 782 985 1212 1512 1851 2291 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A000700 | 1 -1 0 -1 1 -1 1 -1 2 -2 2 -2 3 -3 3 -4 5 -5 5 -6 7 -8 8 -9 11 -12 12 -14 16 -17 18 -20 23 -25 26 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000041 | 1 1 2 3 5 7 11 15 22 30 42 56 77 101 135 176 231 297 385 490 627 792 1002 1255 1575 1958 2436 3010 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A002865 | 1 0 1 1 2 2 4 4 7 8 12 14 21 24 34 41 55 66 88 105 137 165 210 253 320 383 478 574 708 847 1039 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A058397 | 1 1 3 6 13 22 42 66 112 172 270 397 602 858 1245 1748 2464 3381 4671 6302 8537 11372 15147 19914 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A093694 | 1 2 5 9 17 27 46 69 108 158 234 331 476 657 915 1244 1694 2262 3029 3988 5257 6844 8901 11461 14749 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 1 2 2 6 12 60 420 2520 2310 60060 6930 425040 5135130 5811960 3110747640 15075161640 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A064284 | 1 1 1 1 2 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 |
| Std | RowMaxMax k=0..n | T(n, k) | | A002569 | 1 1 1 1 2 2 3 4 5 7 9 11 15 18 23 30 37 47 58 71 90 110 136 164 201 248 300 364 436 525 638 764 919 |
| Std | ColMiddleT(n, n // 2) | A066639 | 1 0 1 1 2 2 3 4 5 6 7 10 11 14 15 21 22 29 30 41 42 55 56 76 77 100 101 134 135 175 176 230 231 296 |
| Std | CentralET(2 n, n) | A000041 | 1 1 2 3 5 7 11 15 22 30 42 56 77 101 135 176 231 297 385 490 627 792 1002 1255 |
| Std | CentralOT(2 n + 1, n) | A000065 | 0 1 2 4 6 10 14 21 29 41 55 76 100 134 175 230 296 384 489 626 791 1001 1254 1574 |
| 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) | 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) | A098545 | 1 1 3 7 21 51 148 365 983 2461 6360 15687 39757 97033 240425 582622 1421273 3409861 8222920 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 -1 1 5 1 4 15 55 139 152 397 1429 2549 3457 9330 26105 48791 86512 207785 520314 1068268 |
| Std | TransNat0∑ k=0..n T(n, k) k | A006128 | 0 1 3 6 12 20 35 54 86 128 192 275 399 556 780 1068 1463 1965 2644 3498 4630 6052 7899 10206 13174 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A093694 | 1 2 5 9 17 27 46 69 108 158 234 331 476 657 915 1244 1694 2262 3029 3988 5257 6844 8901 11461 14749 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | A296010 | 0 1 5 14 34 68 133 232 402 652 1048 1609 2465 3640 5358 7694 10993 15399 21498 29520 40394 54572 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A075900 | 1 1 3 7 19 43 115 259 659 1523 3731 8531 20883 47379 113043 259219 609683 1385363 3245459 7344531 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A352402 | 1 1 -1 3 -1 7 -1 15 31 63 159 95 671 287 3231 2975 15519 7839 44191 34975 224415 291999 863391 |
| 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) | A055642 | 0 1 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 | DiagRow3T(n + 3, n) | A010701 | 0 1 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 |
| Std | DiagCol1T(n + 1, 1) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | DiagCol2T(n + 2, 2) | A004526 | 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 |
| Std | DiagCol3T(n + 3, 3) | A001399 | 1 1 2 3 4 5 7 8 10 12 14 16 19 21 24 27 30 33 37 40 44 48 52 56 61 65 70 75 80 85 91 96 102 108 114 |
| Std | Polysee docs | missing | 1 0 1 0 1 1 0 2 2 1 0 3 6 3 1 0 5 14 12 4 1 0 7 34 39 20 5 1 0 11 74 129 84 30 6 1 0 15 166 399 356 |
| Std | 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 |
| Std | PolyRow2∑ k=0..2 T(2, 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 | PolyRow3∑ k=0..3 T(3, k) n^k | A027444 | 0 3 14 39 84 155 258 399 584 819 1110 1463 1884 2379 2954 3615 4368 5219 6174 7239 8420 9723 11154 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A070933 | 1 2 6 14 34 74 166 350 746 1546 3206 6550 13386 27114 54894 110630 222794 447538 898574 1801590 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A242587 | 1 3 12 39 129 399 1245 3783 11514 34734 104754 314922 946623 2842077 8532147 25603788 76830033 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A124577 | 1 1 6 39 356 4055 57786 983535 19520264 441967518 11235798510 316719689506 9800860032876 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A072233 | 1 0 -1 0 -1 1 0 -1 1 -1 0 -1 2 -1 1 0 -1 2 -2 1 -1 0 -1 3 -3 2 -1 1 0 -1 3 -4 3 -2 1 -1 0 -1 4 -5 5 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 -1 0 1 -1 0 -1 1 -1 0 1 -1 2 -1 0 -1 1 -2 2 -1 0 1 -1 2 -3 3 -1 0 -1 1 -2 3 -4 3 -1 0 1 -1 2 -3 5 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 1 1 0 0 -1 1 0 -1 -3 1 1 0 0 -1 1 -1 1 0 0 -1 2 -3 1 1 0 1 1 1 -2 1 -1 1 0 3 6 0 -4 2 -3 1 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 -1 0 0 1 1 -3 -1 0 1 -1 1 -1 0 0 1 1 -3 2 -1 0 0 1 -1 1 -2 1 1 1 0 1 1 -3 2 -4 0 6 3 |
| Alt | Accsee docs | missing | 1 0 -1 0 -1 0 0 -1 0 -1 0 -1 1 0 1 0 -1 1 -1 0 -1 0 -1 2 -1 1 0 1 0 -1 2 -2 1 -1 0 -1 0 -1 3 -2 3 0 |
| Alt | AccRevsee docs | missing | 1 -1 -1 1 0 0 -1 0 -1 -1 1 0 2 1 1 -1 0 -2 0 -1 -1 1 0 2 -1 2 1 1 -1 0 -2 1 -3 0 -1 -1 1 0 2 -1 4 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 0 -2 0 -2 3 0 -2 3 -4 0 -2 6 -4 5 0 -2 6 -8 5 -6 0 -2 9 -12 10 -6 7 0 -2 9 -16 15 -12 7 -8 0 -2 |
| Alt | RowSum∑ k=0..n T(n, k) | A000700 | 1 -1 0 -1 1 -1 1 -1 2 -2 2 -2 3 -3 3 -4 5 -5 5 -6 7 -8 8 -9 11 -12 12 -14 16 -17 18 -20 23 -25 26 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A027187 | 1 0 1 1 3 3 6 7 12 14 22 27 40 49 69 86 118 146 195 242 317 392 505 623 793 973 1224 1498 1867 2274 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A027193 | 0 -1 -1 -2 -2 -4 -5 -8 -10 -16 -20 -29 -37 -52 -66 -90 -113 -151 -190 -248 -310 -400 -497 -632 -782 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000041 | 1 1 2 3 5 7 11 15 22 30 42 56 77 101 135 176 231 297 385 490 627 792 1002 1255 1575 1958 2436 3010 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000041 | 1 1 2 3 5 7 11 15 22 30 42 56 77 101 135 176 231 297 385 490 627 792 1002 1255 1575 1958 2436 3010 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A298596 | 1 0 -1 -1 0 0 0 0 1 0 0 0 1 0 0 -1 1 0 0 -1 1 -1 0 -1 2 -1 0 -2 2 -1 1 -2 3 -2 1 -3 4 -2 2 -4 5 -3 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -1 -2 1 -2 2 -2 8 -8 10 -9 18 -18 21 -32 44 -45 47 -62 77 -96 99 -118 153 -177 182 -226 269 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -2 1 -3 5 -5 6 -7 12 -14 14 -17 24 -27 27 -36 46 -50 53 -64 77 -88 93 -107 133 -147 154 -180 211 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 1 2 2 6 12 60 420 2520 2310 60060 6930 425040 5135130 5811960 3110747640 15075161640 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A064284 | 1 1 1 1 2 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 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A002569 | 1 1 1 1 2 2 3 4 5 7 9 11 15 18 23 30 37 47 58 71 90 110 136 164 201 248 300 364 436 525 638 764 919 |
| Alt | ColMiddleT(n, n // 2) | A066639 | 1 0 -1 -1 2 2 -3 -4 5 6 -7 -10 11 14 -15 -21 22 29 -30 -41 42 55 -56 -76 77 100 -101 -134 135 175 |
| Alt | CentralET(2 n, n) | A000041 | 1 -1 2 -3 5 -7 11 -15 22 -30 42 -56 77 -101 135 -176 231 -297 385 -490 627 -792 1002 -1255 |
| Alt | CentralOT(2 n + 1, n) | A000065 | 0 -1 2 -4 6 -10 14 -21 29 -41 55 -76 100 -134 175 -230 296 -384 489 -626 791 -1001 1254 -1574 |
| 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 | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 -1 -1 -1 5 -1 4 -15 55 -139 152 -397 1429 -2549 3457 -9330 26105 -48791 86512 -207785 520314 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A098545 | 1 -1 3 -7 21 -51 148 -365 983 -2461 6360 -15687 39757 -97033 240425 -582622 1421273 -3409861 |
| Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 1 -2 4 -4 5 -6 10 -12 12 -15 21 -24 24 -32 41 -45 48 -58 70 -80 85 -98 122 -135 142 -166 195 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -2 1 -3 5 -5 6 -7 12 -14 14 -17 24 -27 27 -36 46 -50 53 -64 77 -88 93 -107 133 -147 154 -180 211 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 3 -6 14 -20 27 -40 62 -84 96 -129 183 -224 250 -326 431 -503 574 -704 878 -1028 1151 -1364 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A352402 | 1 -1 -1 -3 -1 -7 -1 -15 31 -63 159 -95 671 -287 3231 -2975 15519 -7839 44191 -34975 224415 -291999 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A075900 | 1 -1 3 -7 19 -43 115 -259 659 -1523 3731 -8531 20883 -47379 113043 -259219 609683 -1385363 3245459 |
| 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) | A055642 | 0 -1 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 |
| Alt | DiagRow3T(n + 3, n) | A010701 | 0 -1 2 -3 3 -3 3 -3 3 -3 3 -3 3 -3 3 -3 3 -3 3 -3 3 -3 3 -3 3 -3 3 -3 3 -3 3 -3 3 -3 3 -3 3 -3 3 -3 |
| Alt | DiagCol1T(n + 1, 1) | A000012 | -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 |
| Alt | DiagCol2T(n + 2, 2) | A004526 | 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 |
| Alt | DiagCol3T(n + 3, 3) | A001399 | -1 -1 -2 -3 -4 -5 -7 -8 -10 -12 -14 -16 -19 -21 -24 -27 -30 -33 -37 -40 -44 -48 -52 -56 -61 -65 -70 |
| Alt | Polysee docs | missing | 1 0 1 0 -1 1 0 0 -2 1 0 -1 2 -3 1 0 1 -6 6 -4 1 0 -1 14 -21 12 -5 1 0 1 -26 69 -52 20 -6 1 0 -1 50 |
| Alt | 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 |
| Alt | PolyRow2∑ k=0..2 T(2, 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 | PolyRow3∑ k=0..3 T(3, k) n^k | A069778 | 0 -1 -6 -21 -52 -105 -186 -301 -456 -657 -910 -1221 -1596 -2041 -2562 -3165 -3856 -4641 -5526 -6517 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A071109 | 1 -2 2 -6 14 -26 50 -102 214 -426 834 -1678 3398 -6778 13482 -27022 54198 -108306 216346 -432878 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A261582 | 1 -3 6 -21 69 -201 591 -1785 5406 -16194 48426 -145380 436641 -1309611 3927399 -11783280 35354139 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | A292134 | 1 -1 2 -21 220 -2705 40926 -733537 15124216 -352606050 9174382490 -263533561852 8283376452948 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 1 1 0 1 1 2 1 0 1 1 2 2 1 0 1 1 2 3 3 1 0 1 1 2 3 4 3 1 0 1 1 2 3 5 5 4 1 0 1 1 2 3 5 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 0 1 0 -1 1 0 0 -1 1 0 1 -1 -1 1 0 0 1 -1 -1 1 0 0 1 0 -1 -1 1 0 -1 1 1 0 -1 -1 1 0 -1 0 2 0 0 -1 |
| Rev | Accsee docs | missing | 1 1 1 1 2 2 1 2 3 3 1 2 4 5 5 1 2 4 6 7 7 1 2 4 7 10 11 11 1 2 4 7 11 14 15 15 1 2 4 7 12 17 21 22 |
| Rev | AccRevsee docs | missing | 1 0 1 0 1 2 0 1 2 3 0 1 3 4 5 0 1 3 5 6 7 0 1 4 7 9 10 11 0 1 4 8 11 13 14 15 0 1 5 10 15 18 20 21 |
| Rev | AntiDiagsee docs | missing | 1 1 1 0 1 1 1 1 0 1 1 1 1 1 2 0 1 1 2 1 1 1 2 2 0 1 1 2 3 1 1 1 2 3 3 0 1 1 2 3 4 1 1 1 2 3 5 3 0 1 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 2 0 1 2 3 0 1 2 6 4 0 1 2 6 8 5 0 1 2 6 12 15 6 0 1 2 6 12 20 18 7 0 1 2 6 12 25 30 28 8 0 |
| Rev | RowSum∑ k=0..n T(n, k) | A000041 | 1 1 2 3 5 7 11 15 22 30 42 56 77 101 135 176 231 297 385 490 627 792 1002 1255 1575 1958 2436 3010 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A046682 | 1 1 1 2 3 4 6 8 12 16 22 29 40 52 69 90 118 151 195 248 317 400 505 632 793 985 1224 1512 1867 2291 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A000701 | 0 0 1 1 2 3 5 7 10 14 20 27 37 49 66 86 113 146 190 242 310 392 497 623 782 973 1212 1498 1851 2274 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000700 | 1 1 0 1 1 1 1 1 2 2 2 2 3 3 3 4 5 5 5 6 7 8 8 9 11 12 12 14 16 17 18 20 23 25 26 29 33 35 37 41 46 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000041 | 1 1 2 3 5 7 11 15 22 30 42 56 77 101 135 176 231 297 385 490 627 792 1002 1255 1575 1958 2436 3010 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A000009 | 1 1 1 2 2 3 4 5 6 8 10 12 15 18 22 27 32 38 46 54 64 76 89 104 122 142 165 192 222 256 296 340 390 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A093694 | 1 2 5 9 17 27 46 69 108 158 234 331 476 657 915 1244 1694 2262 3029 3988 5257 6844 8901 11461 14749 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A058397 | 1 1 3 6 13 22 42 66 112 172 270 397 602 858 1245 1748 2464 3381 4671 6302 8537 11372 15147 19914 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 1 2 2 6 12 60 420 2520 2310 60060 6930 425040 5135130 5811960 3110747640 15075161640 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A064284 | 1 1 1 1 2 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 |
| Rev | RowMaxMax k=0..n | T(n, k) | | A002569 | 1 1 1 1 2 2 3 4 5 7 9 11 15 18 23 30 37 47 58 71 90 110 136 164 201 248 300 364 436 525 638 764 919 |
| Rev | ColMiddleT(n, n // 2) | A119620 | 1 1 1 1 2 2 3 3 5 5 7 7 11 11 15 15 22 22 30 30 42 42 56 56 77 77 101 101 135 135 176 176 231 231 |
| Rev | CentralET(2 n, n) | A000041 | 1 1 2 3 5 7 11 15 22 30 42 56 77 101 135 176 231 297 385 490 627 792 1002 1255 |
| Rev | CentralOT(2 n + 1, n) | A000041 | 1 1 2 3 5 7 11 15 22 30 42 56 77 101 135 176 231 297 385 490 627 792 1002 1255 |
| 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) | 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 | BinConv∑ k=0..n C(n, k) T(n, k) | A098545 | 1 1 3 7 21 51 148 365 983 2461 6360 15687 39757 97033 240425 582622 1421273 3409861 8222920 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 -1 -1 5 -1 4 -15 55 -139 152 -397 1429 -2549 3457 -9330 26105 -48791 86512 -207785 520314 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A196087 | 0 0 1 3 8 15 31 51 90 142 228 341 525 757 1110 1572 2233 3084 4286 5812 7910 10580 14145 18659 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A058397 | 1 1 3 6 13 22 42 66 112 172 270 397 602 858 1245 1748 2464 3381 4671 6302 8537 11372 15147 19914 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 1 5 18 43 109 211 434 778 1408 2335 3977 6253 9978 15254 23313 34422 51054 73486 105994 149660 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A070933 | 1 2 6 14 34 74 166 350 746 1546 3206 6550 13386 27114 54894 110630 222794 447538 898574 1801590 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A071109 | 1 -2 2 -6 14 -26 50 -102 214 -426 834 -1678 3398 -6778 13482 -27022 54198 -108306 216346 -432878 |
| Rev | DiagRow1T(n + 1, 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 | DiagRow2T(n + 2, n) | A004526 | 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 |
| Rev | DiagRow3T(n + 3, n) | A001399 | 1 1 2 3 4 5 7 8 10 12 14 16 19 21 24 27 30 33 37 40 44 48 52 56 61 65 70 75 80 85 91 96 102 108 114 |
| Rev | 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 |
| Rev | DiagCol2T(n + 2, 2) | A055642 | 0 1 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 | DiagCol3T(n + 3, 3) | A010701 | 0 1 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 |
| Rev | Polysee docs | missing | 1 1 1 1 1 1 1 2 1 1 1 3 3 1 1 1 5 7 4 1 1 1 7 19 13 5 1 1 1 11 43 49 21 6 1 1 1 15 115 157 101 31 7 |
| Rev | 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 |
| Rev | PolyRow2∑ k=0..2 T(2, 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 | PolyRow3∑ k=0..3 T(3, 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 | PolyCol2∑ k=0..n T(n, k) 2^k | A075900 | 1 1 3 7 19 43 115 259 659 1523 3731 8531 20883 47379 113043 259219 609683 1385363 3245459 7344531 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A300579 | 1 1 4 13 49 157 589 1885 6826 22378 78754 256630 904711 2934247 10133851 33287620 113522089 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | A338697 | 1 1 3 13 101 931 12391 178809 3331721 66288142 1589753211 40104031166 1183380156013 36187564837217 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 -1 1 0 0 -1 1 0 1 -1 -1 1 0 0 1 -1 -1 1 0 0 1 0 -1 -1 1 0 -1 1 1 0 -1 -1 1 0 -1 0 2 0 0 -1 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -1 0 1 -1 0 0 1 -1 -1 1 0 1 -1 -1 1 0 0 1 -1 -1 0 1 0 0 1 -1 -1 0 1 1 -1 0 1 -1 -1 0 0 2 0 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 1 0 1 1 1 0 1 1 2 1 0 1 1 2 2 1 0 1 1 2 3 3 1 0 1 1 2 3 4 3 1 0 1 1 2 3 5 5 4 1 0 1 1 2 3 5 |
| Inv | Accsee docs | missing | 1 0 1 0 -1 0 0 0 -1 0 0 1 0 -1 0 0 0 1 0 -1 0 0 0 1 1 0 -1 0 0 -1 0 1 1 0 -1 0 0 -1 -1 1 1 1 0 -1 0 |
| Inv | AccRevsee docs | missing | 1 1 1 1 0 0 1 0 0 0 1 0 -1 0 0 1 0 -1 0 0 0 1 0 -1 -1 0 0 0 1 0 -1 -1 0 1 0 0 1 0 -1 -1 -1 1 1 0 0 |
| Inv | AntiDiagsee docs | missing | 1 0 0 1 0 -1 0 0 1 0 1 -1 0 0 -1 1 0 0 1 -1 0 -1 1 -1 1 0 -1 1 0 -1 0 0 0 1 -1 1 0 0 -1 2 0 -1 0 1 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 -2 3 0 0 -3 4 0 2 -3 -4 5 0 0 3 -4 -5 6 0 0 3 0 -5 -6 7 0 -2 3 4 0 -6 -7 8 0 -2 0 8 0 0 -7 |
| Inv | RowSum∑ k=0..n T(n, k) | A019590 | 1 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 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 0 1 -1 0 0 1 0 0 0 -1 -1 -1 0 0 1 1 2 2 3 3 1 1 -1 -2 -4 -5 -7 -7 -9 -9 -9 -8 -7 -5 -2 1 5 9 15 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -1 1 0 0 -1 0 0 0 1 1 1 0 0 -1 -1 -2 -2 -3 -3 -1 -1 1 2 4 5 7 7 9 9 9 8 7 5 2 -1 -5 -9 -15 -19 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 -1 2 -2 0 0 2 0 0 0 -2 -2 -2 0 0 2 2 4 4 6 6 2 2 -2 -4 -8 -10 -14 -14 -18 -18 -18 -16 -14 -10 -4 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 1 2 2 4 4 4 6 6 6 8 10 10 12 12 14 16 18 20 24 26 28 28 30 36 42 44 46 54 64 72 82 90 90 98 98 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 1 -1 1 0 0 0 0 -1 1 0 -1 1 1 0 0 0 0 0 0 -1 0 -2 -1 -1 0 -2 1 0 1 0 0 3 1 4 2 2 3 5 1 5 2 3 0 2 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -1 -1 0 0 1 0 0 0 -1 -1 -1 0 0 1 1 2 2 3 3 1 1 -1 -2 -4 -5 -7 -7 -9 -9 -9 -8 -7 -5 -2 1 5 9 15 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 1 1 0 0 -1 0 0 0 1 1 1 0 0 -1 -1 -2 -2 -3 -3 -1 -1 1 2 4 5 7 7 9 9 9 8 7 5 2 -1 -5 -9 -15 -19 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 1 1 1 1 1 2 2 2 2 2 2 6 2 12 12 10 30 20 210 210 40 120 168 1980 168 510 72 440 630 6120 3960 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 2 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 1 1 1 1 |
| Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 2 4 4 5 5 5 7 7 8 8 8 11 14 17 18 20 18 18 24 27 31 31 35 33 34 41 54 |
| Inv | ColMiddleT(n, n // 2) | A272901 | 1 0 -1 0 -1 1 0 1 0 2 1 1 0 2 1 1 0 1 0 1 0 1 0 0 -1 1 0 1 0 0 -1 1 0 1 0 1 0 1 0 1 0 1 0 2 1 1 0 1 |
| Inv | CentralOT(2 n + 1, n) | A007706 | 0 0 1 1 2 1 2 1 1 1 1 0 1 1 0 1 1 1 1 1 1 2 1 1 |
| Inv | 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 |
| 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 1 -1 -2 -5 -4 -5 22 69 172 438 925 1805 3290 6268 9336 16645 19109 25141 -1006 -38061 -292116 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 3 4 -5 -14 7 -6 -123 -242 -286 -417 -2067 -4536 -2444 -4470 -26843 -42805 -22895 -56942 -289877 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 1 1 0 0 -1 0 0 0 1 1 1 0 0 -1 -1 -2 -2 -3 -3 -1 -1 1 2 4 5 7 7 9 9 9 8 7 5 2 -1 -5 -9 -15 -19 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 1 1 0 0 -1 0 0 0 1 1 1 0 0 -1 -1 -2 -2 -3 -3 -1 -1 1 2 4 5 7 7 9 9 9 8 7 5 2 -1 -5 -9 -15 -19 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 3 5 4 4 -1 0 -4 -4 -3 1 1 4 8 7 11 6 6 -3 -7 -13 -17 -23 -26 -32 -31 -25 -25 -11 -3 13 24 51 61 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 -1 -1 3 3 11 -21 -69 -69 -293 -37 283 3867 9627 19867 35483 47771 42139 -47973 -419685 -2418533 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 1 3 3 -9 -9 15 -81 63 63 -609 1695 -2337 8415 -11169 -5025 71007 -162465 533343 -1211553 3000159 |
| Inv | 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 |
| Inv | DiagRow2T(n + 2, n) | A000012 | 0 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 |
| Inv | DiagRow3T(n + 3, n) | A039966 | 0 1 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 |
| Inv | DiagCol1T(n + 1, 1) | A039800 | 1 -1 0 1 0 0 -1 -1 0 0 1 1 2 2 1 0 -1 -2 -3 -4 -5 -5 -5 -4 -3 -1 2 5 8 11 14 17 18 20 20 20 18 16 |
| Inv | DiagCol2T(n + 2, 2) | A039801 | 1 -1 -1 1 1 1 0 -1 -2 -2 -1 -1 0 2 4 4 5 5 5 2 1 -2 -5 -8 -11 -14 -17 -18 -20 -18 -18 -11 -9 -1 4 |
| Inv | DiagCol3T(n + 3, 3) | A039802 | 1 -1 -1 0 1 2 0 1 -1 -2 -2 -3 -2 -2 1 1 3 4 7 7 8 8 7 5 2 -1 -6 -8 -15 -18 -24 -27 -31 -31 -35 -33 |
| Inv | Polysee docs | missing | 1 0 1 0 1 1 0 0 2 1 0 0 2 3 1 0 0 4 6 4 1 0 0 6 18 12 5 1 0 0 12 48 48 20 6 1 0 0 20 144 180 100 30 |
| 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 |
| Inv | PolyRow2∑ k=0..2 T(2, 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 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | A045991 | 0 0 4 18 48 100 180 294 448 648 900 1210 1584 2028 2548 3150 3840 4624 5508 6498 7600 8820 10164 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 2 4 6 12 20 42 78 156 304 610 1198 2400 4764 9530 18992 37990 75832 151686 303084 606182 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 6 18 48 144 414 1248 3696 11088 33138 99426 297858 893616 2679648 8038974 24113358 72340188 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 2 18 180 2400 37620 689472 14418936 339603840 8900110800 257018244010 8111211039228 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 0 1 -1 0 1 -1 0 0 1 -1 -1 1 0 1 -1 -1 1 0 0 1 -1 -1 0 1 0 0 1 -1 -1 0 1 1 -1 0 1 -1 -1 0 0 2 0 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 0 1 0 -1 1 0 0 -1 1 0 1 -1 -1 1 0 0 1 -1 -1 1 0 0 1 0 -1 -1 1 0 -1 1 1 0 -1 -1 1 0 -1 0 2 0 0 -1 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A072233 | 1 0 1 0 1 1 0 1 1 1 0 1 2 1 1 0 1 2 2 1 1 0 1 3 3 2 1 1 0 1 3 4 3 2 1 1 0 1 4 5 5 3 2 1 1 0 1 4 7 6 |
| Inv:Rev | Accsee docs | missing | 1 1 1 1 0 0 1 0 0 0 1 0 -1 0 0 1 0 -1 0 0 0 1 0 -1 -1 0 0 0 1 0 -1 -1 0 1 0 0 1 0 -1 -1 -1 1 1 0 0 |
| Inv:Rev | AccRevsee docs | missing | 1 0 1 0 -1 0 0 0 -1 0 0 1 0 -1 0 0 0 1 0 -1 0 0 0 1 1 0 -1 0 0 -1 0 1 1 0 -1 0 0 -1 -1 1 1 1 0 -1 0 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 -1 1 -1 0 1 -1 0 1 -1 -1 0 1 -1 -1 1 1 -1 -1 1 0 1 -1 -1 0 0 1 -1 -1 0 1 0 1 -1 -1 0 1 0 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 -2 0 1 -2 0 0 1 -2 -3 4 0 1 -2 -3 4 0 0 1 -2 -3 0 5 0 0 1 -2 -3 0 5 6 -7 0 1 -2 -3 0 0 12 0 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A019590 | 1 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 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 1 1 0 0 1 0 0 0 -1 1 -1 0 0 -1 1 -2 2 -3 3 -1 1 1 -2 4 -5 7 -7 9 -9 9 -8 7 -5 2 1 -5 9 -15 19 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 -1 -1 0 0 -1 0 0 0 1 -1 1 0 0 1 -1 2 -2 3 -3 1 -1 -1 2 -4 5 -7 7 -9 9 -9 8 -7 5 -2 -1 5 -9 15 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 1 2 2 0 0 2 0 0 0 -2 2 -2 0 0 -2 2 -4 4 -6 6 -2 2 2 -4 8 -10 14 -14 18 -18 18 -16 14 -10 4 2 -10 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | missing | 1 1 2 2 4 4 4 6 6 6 8 10 10 12 12 14 16 18 20 24 26 28 28 30 36 42 44 46 54 64 72 82 90 90 98 98 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 0 0 0 -1 0 0 -1 0 0 0 0 1 -1 0 2 -1 1 0 0 0 1 -1 0 0 0 0 -1 0 -1 2 -3 2 -3 1 -2 3 -2 1 -1 1 0 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 1 1 0 0 -1 0 0 0 1 1 1 0 0 -1 -1 -2 -2 -3 -3 -1 -1 1 2 4 5 7 7 9 9 9 8 7 5 2 -1 -5 -9 -15 -19 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -1 -1 0 0 1 0 0 0 -1 -1 -1 0 0 1 1 2 2 3 3 1 1 -1 -2 -4 -5 -7 -7 -9 -9 -9 -8 -7 -5 -2 1 5 9 15 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 1 1 1 1 1 1 2 2 2 2 2 2 6 2 12 12 10 30 20 210 210 40 120 168 1980 168 510 72 440 630 6120 3960 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 2 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 1 1 1 1 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 2 4 4 5 5 5 7 7 8 8 8 11 14 17 18 20 18 18 24 27 31 31 35 33 34 41 54 |
| Inv:Rev | ColMiddleT(n, n // 2) | A000012 | 1 1 -1 -1 -1 -1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 |
| 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 | 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 |
| Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 -1 -2 -5 -4 -5 22 69 172 438 925 1805 3290 6268 9336 16645 19109 25141 -1006 -38061 -292116 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 3 -4 -5 14 7 6 -123 242 -286 417 -2067 4536 -2444 4470 -26843 42805 -22895 56942 -289877 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 -1 -1 0 0 1 0 0 0 -1 -1 -1 0 0 1 1 2 2 3 3 1 1 -1 -2 -4 -5 -7 -7 -9 -9 -9 -8 -7 -5 -2 1 5 9 15 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -1 -1 0 0 1 0 0 0 -1 -1 -1 0 0 1 1 2 2 3 3 1 1 -1 -2 -4 -5 -7 -7 -9 -9 -9 -8 -7 -5 -2 1 5 9 15 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -1 -1 4 4 11 0 -4 -4 -23 -21 -23 4 8 37 43 74 78 111 113 29 27 -69 -122 -232 -291 -403 -417 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 2 2 4 6 12 20 42 78 156 304 610 1198 2400 4764 9530 18992 37990 75832 151686 303084 606182 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 6 -12 18 -36 84 -162 306 -612 1248 -2514 4938 -9864 19908 -39786 79248 -158502 317616 -635166 |
| Inv:Rev | DiagRow1T(n + 1, n) | A039800 | 1 -1 0 1 0 0 -1 -1 0 0 1 1 2 2 1 0 -1 -2 -3 -4 -5 -5 -5 -4 -3 -1 2 5 8 11 14 17 18 20 20 20 18 16 |
| Inv:Rev | DiagRow2T(n + 2, n) | A039801 | 1 -1 -1 1 1 1 0 -1 -2 -2 -1 -1 0 2 4 4 5 5 5 2 1 -2 -5 -8 -11 -14 -17 -18 -20 -18 -18 -11 -9 -1 4 |
| Inv:Rev | DiagRow3T(n + 3, n) | A039802 | 1 -1 -1 0 1 2 0 1 -1 -2 -2 -3 -2 -2 1 1 3 4 7 7 8 8 7 5 2 -1 -6 -8 -15 -18 -24 -27 -31 -31 -35 -33 |
| Inv:Rev | 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 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A000012 | 0 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 |
| Inv:Rev | DiagCol3T(n + 3, 3) | A039966 | 0 1 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 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 0 1 1 1 0 -1 1 1 1 0 -1 -2 1 1 1 0 3 -2 -3 1 1 1 0 3 16 -3 -4 1 1 1 0 11 16 45 -4 -5 |
| Inv:Rev | 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 |
| Inv:Rev | PolyRow2∑ k=0..2 T(2, 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 | PolyRow3∑ k=0..3 T(3, 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 | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 -1 -1 3 3 11 -21 -69 -69 -293 -37 283 3867 9627 19867 35483 47771 42139 -47973 -419685 -2418533 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 -2 -2 16 16 70 -416 -1712 -1712 -9974 16270 83338 752560 2607136 6504370 14193862 13130980 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 -1 -2 45 96 1255 -98496 -2031687 -4664960 -188900109 21028589990 670843358053 44517814236000 |
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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.