OEIS Similars: A050446, A050447
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A050446 | 1 1 1 1 2 1 1 3 3 1 1 5 6 4 1 1 8 14 10 5 1 1 13 31 30 15 6 1 1 21 70 85 55 21 7 1 1 34 157 246 190 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A050447 | 1 1 1 1 2 1 1 3 3 1 1 4 6 5 1 1 5 10 14 8 1 1 6 15 30 31 13 1 1 7 21 55 85 70 21 1 1 8 28 91 190 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 1 -2 1 -1 3 -3 1 2 -5 6 -4 1 -7 15 -14 10 -5 1 23 -56 53 -30 15 -6 1 -89 216 -222 135 -55 21 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -2 1 1 -3 3 -1 1 -4 6 -5 2 1 -5 10 -14 15 -7 1 -6 15 -30 53 -56 23 1 -7 21 -55 135 -222 |
| Std | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 -1 1 1 -2 1 -1 3 -3 1 2 -7 9 -5 1 -8 29 -40 26 -8 1 62 -226 316 -213 73 -13 1 -872 3181 -4457 |
| Std | Accsee docs | missing | 1 1 2 1 3 4 1 4 7 8 1 6 12 16 17 1 9 23 33 38 39 1 14 45 75 90 96 97 1 22 92 177 232 253 260 261 1 |
| Std | AccRevsee docs | missing | 1 1 2 1 3 4 1 4 7 8 1 5 11 16 17 1 6 16 30 38 39 1 7 22 52 83 96 97 1 8 29 84 169 239 260 261 1 9 |
| Std | AntiDiagsee docs | missing | 1 1 1 1 1 2 1 3 1 1 5 3 1 8 6 1 1 13 14 4 1 21 31 10 1 1 34 70 30 5 1 55 157 85 15 1 1 89 353 246 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 4 3 1 6 9 4 1 10 18 16 5 1 16 42 40 25 6 1 26 93 120 75 36 7 1 42 210 340 275 126 49 8 1 68 |
| Std | RowSum∑ k=0..n T(n, k) | A373353 | 1 2 4 8 17 39 97 261 756 2344 7738 27070 99946 388085 1579914 6725192 29860100 137991971 662439670 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 2 4 8 20 48 133 377 1174 3851 13515 49929 194227 790745 3365052 14931138 68975214 331087761 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 2 4 9 19 49 128 379 1170 3887 13555 50017 193858 789169 3360140 14928962 69016757 331351909 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 0 0 0 -1 1 -1 5 -2 4 -36 -40 -88 369 1576 4912 2176 -41543 -264148 -806873 -595949 10318215 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A373353 | 1 2 4 8 17 39 97 261 756 2344 7738 27070 99946 388085 1579914 6725192 29860100 137991971 662439670 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 2 3 5 9 16 32 64 140 314 750 1857 4822 12999 36461 105980 319073 992921 3190257 10568217 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 8 20 52 143 418 1298 4271 14846 54349 208945 841373 3540134 15530141 70890502 336096392 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 8 20 50 130 358 1051 3289 10938 38507 142965 557871 2281141 9748483 43437762 201385408 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 3 60 280 12090 39270 22704328920 1597588825140 1247472060421860 407481614227915920 |
| Std | 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 |
| Std | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 3 6 14 31 85 246 707 2353 8272 29056 110254 457379 1897214 7911970 37846314 181033035 |
| Std | ColMiddleT(n, n // 2) | missing | 1 1 2 3 6 14 30 85 190 671 1547 6405 15106 72302 173502 940005 2286648 13846117 34053437 227837533 |
| Std | CentralET(2 n, n) | A373659 | 1 2 6 30 190 1547 15106 173502 2286648 34053437 565424068 10358963615 207582616995 4516836844067 |
| Std | CentralOT(2 n + 1, n) | A276313 | 1 3 14 85 671 6405 72302 940005 13846117 227837533 4142793511 82488063476 1785049505682 |
| 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) | 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) | missing | 1 2 6 20 74 307 1406 7009 37690 217022 1329776 8626345 58991663 423720650 3186522523 25020668538 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -2 0 2 -25 -22 119 -726 -1170 10268 -47025 -95041 1340794 -6285277 -9837602 255629450 |
| Std | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 4 12 33 91 261 790 2533 8594 30769 115895 457925 1893056 8168569 36712570 171525308 831608377 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 8 20 50 130 358 1051 3289 10938 38507 142965 557871 2281141 9748483 43437762 201385408 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 6 24 81 259 833 2772 9655 35302 135391 543559 2279305 9961822 45291285 213826724 1046589490 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 3 9 27 89 323 1289 5611 26425 133715 722793 4152955 25254809 161938275 1091314633 7707065867 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -1 1 -1 -7 15 -47 -33 489 -2897 7873 -641 -181415 1351247 -5979471 8990495 121190345 -1490978833 |
| 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) | A000217 | 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Std | DiagRow3T(n + 3, n) | A000330 | 1 5 14 30 55 91 140 204 285 385 506 650 819 1015 1240 1496 1785 2109 2470 2870 3311 3795 4324 4900 |
| Std | DiagCol1T(n + 1, 1) | A000045 | 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 |
| Std | DiagCol2T(n + 2, 2) | A006356 | 1 3 6 14 31 70 157 353 793 1782 4004 8997 20216 45425 102069 229347 515338 1157954 2601899 5846414 |
| Std | DiagCol3T(n + 3, 3) | A006357 | 1 4 10 30 85 246 707 2037 5864 16886 48620 139997 403104 1160693 3342081 9623140 27708726 79784098 |
| Std | Polysee docs | missing | 1 1 1 1 2 1 1 4 3 1 1 8 9 4 1 1 17 27 16 5 1 1 39 83 64 25 6 1 1 97 265 259 125 36 7 1 1 261 887 |
| 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 | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | A000578 | 1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 9261 10648 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 3 9 27 83 265 887 3131 11689 46171 192687 847577 3918515 18986199 96152221 507714475 2789068855 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 4 16 64 259 1069 4531 19837 90130 426460 2105872 10862020 58510204 328830865 1925302972 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 9 64 629 7891 120427 2164821 44790865 1048283704 27378347191 789331696220 24898416058285 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A050446 | 1 1 -1 1 -2 1 1 -3 3 -1 1 -5 6 -4 1 1 -8 14 -10 5 -1 1 -13 31 -30 15 -6 1 1 -21 70 -85 55 -21 7 -1 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A050447 | 1 -1 1 1 -2 1 -1 3 -3 1 1 -4 6 -5 1 -1 5 -10 14 -8 1 1 -6 15 -30 31 -13 1 -1 7 -21 55 -85 70 -21 1 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -3 2 1 5 -3 -3 1 32 -19 -18 4 1 -77 45 46 -10 -5 1 -713 416 425 -90 -45 6 1 2227 -1296 -1344 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 2 -3 1 -3 -3 5 1 4 -18 -19 32 1 -5 -10 46 45 -77 1 6 -45 -90 425 416 -713 1 -7 -21 155 285 |
| Alt | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 1 1 1 2 1 1 3 3 1 2 7 9 5 1 8 29 40 26 8 1 62 226 316 213 73 13 1 872 3181 4457 3023 1058 203 21 |
| Alt | Accsee docs | missing | 1 1 0 1 -1 0 1 -2 1 0 1 -4 2 -2 -1 1 -7 7 -3 2 1 1 -12 19 -11 4 -2 -1 1 -20 50 -35 20 -1 6 5 1 -33 |
| Alt | AccRevsee docs | missing | 1 -1 0 1 -1 0 -1 2 -1 0 1 -3 3 -2 -1 -1 4 -6 8 0 1 1 -5 10 -20 11 -2 -1 -1 6 -15 40 -45 25 4 5 1 -7 |
| Alt | AntiDiagsee docs | missing | 1 1 1 -1 1 -2 1 -3 1 1 -5 3 1 -8 6 -1 1 -13 14 -4 1 -21 31 -10 1 1 -34 70 -30 5 1 -55 157 -85 15 -1 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -4 3 1 -6 9 -4 1 -10 18 -16 5 1 -16 42 -40 25 -6 1 -26 93 -120 75 -36 7 1 -42 210 -340 275 |
| Alt | RowSum∑ k=0..n T(n, k) | missing | 1 0 0 0 -1 1 -1 5 -2 4 -36 -40 -88 369 1576 4912 2176 -41543 -264148 -806873 -595949 10318215 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 2 4 8 20 48 133 377 1174 3851 13515 49929 194227 790745 3365052 14931138 68975214 331087761 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -2 -4 -9 -19 -49 -128 -379 -1170 -3887 -13555 -50017 -193858 -789169 -3360140 -14928962 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A373353 | 1 2 4 8 17 39 97 261 756 2344 7738 27070 99946 388085 1579914 6725192 29860100 137991971 662439670 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A373353 | 1 2 4 8 17 39 97 261 756 2344 7738 27070 99946 388085 1579914 6725192 29860100 137991971 662439670 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -1 -1 -1 -2 -2 2 12 32 68 113 100 -227 -1641 -6116 -17693 -41137 -66101 11991 699067 3910549 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 0 0 -4 1 -2 26 15 30 -259 -637 -1419 2378 20061 78954 113908 -413293 -4107541 -16532135 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 0 0 -2 6 -6 19 -35 14 -173 117 187 3157 5155 4550 -74740 -376024 -1175419 -412198 16302102 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 3 60 280 12090 39270 22704328920 1597588825140 1247472060421860 407481614227915920 |
| Alt | 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 |
| Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 3 6 14 31 85 246 707 2353 8272 29056 110254 457379 1897214 7911970 37846314 181033035 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 1 -2 -3 6 14 -30 -85 190 671 -1547 -6405 15106 72302 -173502 -940005 2286648 13846117 -34053437 |
| Alt | CentralET(2 n, n) | A373659 | 1 -2 6 -30 190 -1547 15106 -173502 2286648 -34053437 565424068 -10358963615 207582616995 |
| Alt | CentralOT(2 n + 1, n) | A276313 | 1 -3 14 -85 671 -6405 72302 -940005 13846117 -227837533 4142793511 -82488063476 1785049505682 |
| 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 | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -2 0 2 25 -22 -119 -726 1170 10268 47025 -95041 -1340794 -6285277 9837602 255629450 1484849207 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 6 -20 74 -307 1406 -7009 37690 -217022 1329776 -8626345 58991663 -423720650 3186522523 |
| Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 0 0 -1 5 -5 14 -33 10 -137 157 275 2788 3579 -362 -76916 -334481 -911271 394675 16898051 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 0 0 -2 6 -6 19 -35 14 -173 117 187 3157 5155 4550 -74740 -376024 -1175419 -412198 16302102 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 2 0 -1 13 -33 52 -175 226 -415 1889 599 8330 -20813 -88180 -483586 -751765 1589475 27058795 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 1 1 -7 -15 -47 33 489 2897 7873 641 -181415 -1351247 -5979471 -8990495 121190345 1490978833 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -3 9 -27 89 -323 1289 -5611 26425 -133715 722793 -4152955 25254809 -161938275 1091314633 |
| 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) | A000217 | 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 |
| Alt | DiagRow3T(n + 3, n) | A000330 | 1 -5 14 -30 55 -91 140 -204 285 -385 506 -650 819 -1015 1240 -1496 1785 -2109 2470 -2870 3311 -3795 |
| Alt | DiagCol1T(n + 1, 1) | A000045 | -1 -2 -3 -5 -8 -13 -21 -34 -55 -89 -144 -233 -377 -610 -987 -1597 -2584 -4181 -6765 -10946 -17711 |
| Alt | DiagCol2T(n + 2, 2) | A006356 | 1 3 6 14 31 70 157 353 793 1782 4004 8997 20216 45425 102069 229347 515338 1157954 2601899 5846414 |
| Alt | DiagCol3T(n + 3, 3) | A006357 | -1 -4 -10 -30 -85 -246 -707 -2037 -5864 -16886 -48620 -139997 -403104 -1160693 -3342081 -9623140 |
| Alt | Polysee docs | missing | 1 1 1 1 0 1 1 0 -1 1 1 0 1 -2 1 1 -1 -1 4 -3 1 1 1 -1 -8 9 -4 1 1 -1 9 13 -27 16 -5 1 1 5 -29 -5 77 |
| 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 | A000290 | 1 0 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | A000578 | 1 0 -1 -8 -27 -64 -125 -216 -343 -512 -729 -1000 -1331 -1728 -2197 -2744 -3375 -4096 -4913 -5832 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -1 1 -1 -1 9 -29 87 -255 655 -1733 4825 -11921 32435 -96123 223679 -712141 2347829 -4061537 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 4 -8 13 -5 -83 541 -2576 10816 -42458 162082 -607370 2240869 -8267834 30542320 -112498940 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 1 -8 77 -939 13999 -246763 5020209 -115777196 2984871411 -85070702870 2655933577429 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A050447 | 1 1 1 1 2 1 1 3 3 1 1 4 6 5 1 1 5 10 14 8 1 1 6 15 30 31 13 1 1 7 21 55 85 70 21 1 1 8 28 91 190 |
| Rev | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 1 -2 1 -1 3 -3 1 2 -7 9 -5 1 -8 29 -40 26 -8 1 62 -226 316 -213 73 -13 1 -872 3181 -4457 |
| Rev | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -2 1 1 -3 3 -1 1 -5 9 -7 2 1 -8 26 -40 29 -8 1 -13 73 -213 316 -226 62 1 -21 203 -1058 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 -1 1 1 -2 1 -1 3 -3 1 2 -5 6 -4 1 -7 15 -14 10 -5 1 23 -56 53 -30 15 -6 1 -89 216 -222 135 -55 21 |
| Rev | Accsee docs | missing | 1 1 2 1 3 4 1 4 7 8 1 5 11 16 17 1 6 16 30 38 39 1 7 22 52 83 96 97 1 8 29 84 169 239 260 261 1 9 |
| Rev | AccRevsee docs | missing | 1 1 2 1 3 4 1 4 7 8 1 6 12 16 17 1 9 23 33 38 39 1 14 45 75 90 96 97 1 22 92 177 232 253 260 261 1 |
| Rev | AntiDiagsee docs | missing | 1 1 1 1 1 2 1 3 1 1 4 3 1 5 6 1 1 6 10 5 1 7 15 14 1 1 8 21 30 8 1 9 28 55 31 1 1 10 36 91 85 13 1 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 4 3 1 6 9 4 1 8 18 20 5 1 10 30 56 40 6 1 12 45 120 155 78 7 1 14 63 220 425 420 147 8 1 16 |
| Rev | RowSum∑ k=0..n T(n, k) | A373353 | 1 2 4 8 17 39 97 261 756 2344 7738 27070 99946 388085 1579914 6725192 29860100 137991971 662439670 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 2 4 8 19 48 128 377 1170 3851 13555 49929 193858 790745 3360140 14931138 69016757 331087761 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 2 4 9 20 49 133 379 1174 3887 13515 50017 194227 789169 3365052 14928962 68975214 331351909 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 0 0 0 -1 -1 -1 -5 -2 -4 -36 40 -88 -369 1576 -4912 2176 41543 -264148 806873 -595949 -10318215 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A373353 | 1 2 4 8 17 39 97 261 756 2344 7738 27070 99946 388085 1579914 6725192 29860100 137991971 662439670 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 2 3 5 8 13 22 38 68 125 236 458 910 1852 3852 8179 17715 39087 87806 200637 466010 1099533 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 8 20 50 130 358 1051 3289 10938 38507 142965 557871 2281141 9748483 43437762 201385408 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 8 20 52 143 418 1298 4271 14846 54349 208945 841373 3540134 15530141 70890502 336096392 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 3 60 280 12090 39270 22704328920 1597588825140 1247472060421860 407481614227915920 |
| 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 |
| Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 3 6 14 31 85 246 707 2353 8272 29056 110254 457379 1897214 7911970 37846314 181033035 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 2 3 6 10 30 55 190 371 1547 3164 15106 31998 173502 377739 2286648 5089282 34053437 77173602 |
| Rev | CentralET(2 n, n) | A373659 | 1 2 6 30 190 1547 15106 173502 2286648 34053437 565424068 10358963615 207582616995 4516836844067 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 3 10 55 371 3164 31998 377739 5089282 77173602 1300879372 24139773879 489072813581 10743613768108 |
| 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) | 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 2 6 20 74 307 1406 7009 37690 217022 1329776 8626345 58991663 423720650 3186522523 25020668538 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -2 0 2 25 -22 -119 -726 1170 10268 47025 -95041 -1340794 -6285277 9837602 255629450 1484849207 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 4 12 35 104 321 1037 3515 12502 46611 181875 741427 3152049 13950227 64165310 306236292 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 8 20 52 143 418 1298 4271 14846 54349 208945 841373 3540134 15530141 70890502 336096392 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 6 24 89 324 1193 4501 17511 70474 293811 1269339 5681329 26328731 126234497 625617824 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 3 9 27 83 265 887 3131 11689 46171 192687 847577 3918515 18986199 96152221 507714475 2789068855 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -1 1 -1 -1 9 -29 87 -255 655 -1733 4825 -11921 32435 -96123 223679 -712141 2347829 -4061537 |
| Rev | DiagRow1T(n + 1, n) | A000045 | 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 |
| Rev | DiagRow2T(n + 2, n) | A006356 | 1 3 6 14 31 70 157 353 793 1782 4004 8997 20216 45425 102069 229347 515338 1157954 2601899 5846414 |
| Rev | DiagRow3T(n + 3, n) | A006357 | 1 4 10 30 85 246 707 2037 5864 16886 48620 139997 403104 1160693 3342081 9623140 27708726 79784098 |
| 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) | A000217 | 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Rev | DiagCol3T(n + 3, 3) | A000330 | 1 5 14 30 55 91 140 204 285 385 506 650 819 1015 1240 1496 1785 2109 2470 2870 3311 3795 4324 4900 |
| Rev | Polysee docs | missing | 1 1 1 1 2 1 1 4 3 1 1 8 9 4 1 1 17 27 16 5 1 1 39 89 64 25 6 1 1 97 323 283 125 36 7 1 1 261 1289 |
| 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 | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A000578 | 1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 9261 10648 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 3 9 27 89 323 1289 5611 26425 133715 722793 4152955 25254809 161938275 1091314633 7707065867 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 4 16 64 283 1375 7363 43087 273274 1865188 13619128 105854164 871982020 7583712547 69400714084 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 9 64 689 10151 194977 4694691 138124609 4861268056 201184488601 9652234655020 530574979156849 |
| Rev:Inv | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 1 -2 1 -1 3 -3 1 2 -7 9 -5 1 -8 29 -40 26 -8 1 62 -226 316 -213 73 -13 1 -872 3181 -4457 |
| Rev:Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -2 1 1 -3 3 -1 1 -5 9 -7 2 1 -8 26 -40 29 -8 1 -13 73 -213 316 -226 62 1 -21 203 -1058 |
| Rev:Inv | InvT-1(n, k), 0 ≤ k ≤ n | A050447 | 1 1 1 1 2 1 1 3 3 1 1 4 6 5 1 1 5 10 14 8 1 1 6 15 30 31 13 1 1 7 21 55 85 70 21 1 1 8 28 91 190 |
| Rev:Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A050446 | 1 1 1 1 2 1 1 3 3 1 1 5 6 4 1 1 8 14 10 5 1 1 13 31 30 15 6 1 1 21 70 85 55 21 7 1 1 34 157 246 190 |
| Rev:Inv | AccRevsee docs | missing | 1 1 0 1 -1 0 1 -2 1 0 1 -4 5 -2 0 1 -7 19 -21 8 0 1 -12 61 -152 164 -62 0 1 -20 183 -875 2148 -2309 |
| Rev:Inv | AntiDiagsee docs | missing | 1 -1 1 1 -1 -2 2 3 1 -8 -7 -3 62 29 9 1 -872 -226 -40 -5 21572 3181 316 26 1 -917740 -78701 -4457 |
| Rev:Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 1 -4 3 -1 6 -9 4 2 -14 27 -20 5 -8 58 -120 104 -40 6 62 -452 948 -852 365 -78 7 -872 6362 |
| Rev:Inv | RowSum∑ k=0..n T(n, 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 | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 -1 2 -4 12 -56 452 -6408 158720 -6753520 487267332 -59012180140 11908411586836 -3981557097706600 |
| Rev:Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -2 4 -12 56 -452 6408 -158720 6753520 -487267332 59012180140 -11908411586836 3981557097706600 |
| Rev:Inv | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 -2 4 -8 24 -112 904 -12816 317440 -13507040 974534664 -118024360280 23816823173672 |
| Rev:Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 2 4 8 24 112 904 12816 317440 13507040 974534664 118024360280 23816823173672 7963114195413200 |
| Rev:Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 -1 2 -3 6 -18 101 -1143 25096 -1001119 69675493 -8265382904 1647807224934 -546990501644757 |
| Rev:Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | 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 |
| Rev:Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 3 630 15080 223755147876 12040205514667172472 2970962282990634403741413277932 |
| Rev: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 |
| Rev:Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 3 9 40 316 4457 110301 4692761 338578922 41004707820 8274577913085 2766590984097352 |
| Rev:Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -2 3 9 -40 -213 3023 26289 -1119035 -15714012 1903142689 42245894352 -14124853454696 |
| Rev:Inv | CentralET(2 n, n) | missing | 1 -2 9 -213 26289 -15714012 42245894352 -496485380259869 25020970232548585825 |
| Rev:Inv | CentralOT(2 n + 1, n) | missing | -1 3 -40 3023 -1119035 1903142689 -14124853454696 450211096611649614 -60855902279185430879615 |
| Rev:Inv | ColLeftT(n, 0) | missing | 1 -1 1 -1 2 -8 62 -872 21572 -917740 66213870 -8019043354 1618209217426 -541045484536628 |
| 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 0 -2 0 9 -42 204 690 -143213 12385161 -1352285513 211974678595 -49480913783175 17320173775271076 |
| Rev:Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 6 20 105 854 11592 263982 10074867 638117315 66594768955 11385996909027 3176676780507841 |
| Rev:Inv | TransNat0∑ k=0..n T(n, k) k | A063524 | 0 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 |
| Rev:Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | 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 |
| Rev:Inv | TransSqrs∑ k=0..n T(n, k) k^2 | A039968 | 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 -1 1 -1 3 -23 355 -9981 493801 -42015361 6062713767 -1468488725287 592669691361503 |
| Rev:Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 3 9 27 135 1161 18279 515511 25515297 2171098539 313286022027 75883057042617 30625764762039939 |
| Rev:Inv | DiagRow1T(n + 1, n) | A000045 | -1 -2 -3 -5 -8 -13 -21 -34 -55 -89 -144 -233 -377 -610 -987 -1597 -2584 -4181 -6765 -10946 -17711 |
| Rev:Inv | DiagRow2T(n + 2, n) | missing | 1 3 9 26 73 203 557 1517 4102 11034 29548 78844 209754 556645 1474170 3897301 10288366 27126511 |
| Rev:Inv | DiagRow3T(n + 3, n) | missing | -1 -7 -40 -213 -1058 -5107 -23929 -110088 -498542 -2231452 -9892648 -43524509 -190305077 -827860668 |
| Rev:Inv | DiagCol1T(n + 1, 1) | missing | 1 -2 3 -7 29 -226 3181 -78701 3348225 -241570840 29256216062 -5903781403843 1973919217997404 |
| Rev:Inv | DiagCol2T(n + 2, 2) | missing | 1 -3 9 -40 316 -4457 110301 -4692761 338578922 -41004707820 8274577913085 -2766590984097352 |
| Rev:Inv | DiagCol3T(n + 3, 3) | missing | 1 -5 26 -213 3023 -74878 3186031 -229872303 27839469872 -5617888737865 1878331513607302 |
| Rev:Inv | Polysee docs | missing | 1 -1 1 1 0 1 -1 0 1 1 2 0 1 2 1 -8 0 1 4 3 1 62 0 0 8 9 4 1 -872 0 2 8 27 16 5 1 21572 0 -14 16 54 |
| Rev: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 |
| Rev:Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A000290 | 1 0 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 |
| Rev:Inv | PolyRow3∑ k=0..3 T(3, k) n^k | A000578 | -1 0 1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 9261 |
| Rev:Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 1 1 0 2 -14 198 -4898 208378 -15034242 1820770306 -367423791496 122847516421780 |
| Rev:Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 2 4 8 8 16 -40 688 -16864 717632 -51776232 6270528056 -1265366204072 423073026910864 |
| Rev:Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 1 8 54 512 4250 64368 -64484 46177280 -3620775330 538522207000 -128363298008066 |
| << | 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.