OEIS Similars: A003506
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A003506 | 1 2 2 3 6 3 4 12 12 4 5 20 30 20 5 6 30 60 60 30 6 7 42 105 140 105 42 7 8 56 168 280 280 168 56 8 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A003506 | 1 2 2 3 6 3 4 12 12 4 5 20 30 20 5 6 30 60 60 30 6 7 42 105 140 105 42 7 8 56 168 280 280 168 56 8 |
| Std | Accsee docs | missing | 1 2 4 3 9 12 4 16 28 32 5 25 55 75 80 6 36 96 156 186 192 7 49 154 294 399 441 448 8 64 232 512 792 |
| Std | AccRevsee docs | missing | 1 2 4 3 9 12 4 16 28 32 5 25 55 75 80 6 36 96 156 186 192 7 49 154 294 399 441 448 8 64 232 512 792 |
| Std | AntiDiagsee docs | A128502 | 1 2 3 2 4 6 5 12 3 6 20 12 7 30 30 4 8 42 60 20 9 56 105 60 5 10 72 168 140 30 11 90 252 280 105 6 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 2 4 3 12 9 4 24 36 16 5 40 90 80 25 6 60 180 240 150 36 7 84 315 560 525 252 49 8 112 504 1120 |
| Std | RowSum∑ k=0..n T(n, k) | A001787 | 1 4 12 32 80 192 448 1024 2304 5120 11264 24576 53248 114688 245760 524288 1114112 2359296 4980736 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A057711 | 1 2 6 16 40 96 224 512 1152 2560 5632 12288 26624 57344 122880 262144 557056 1179648 2490368 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A057711 | 0 2 6 16 40 96 224 512 1152 2560 5632 12288 26624 57344 122880 262144 557056 1179648 2490368 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^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 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A001787 | 1 4 12 32 80 192 448 1024 2304 5120 11264 24576 53248 114688 245760 524288 1114112 2359296 4980736 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A001629 | 1 2 5 10 20 38 71 130 235 420 744 1308 2285 3970 6865 11822 20284 34690 59155 100610 170711 289032 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A001788 | 1 6 24 80 240 672 1792 4608 11520 28160 67584 159744 372736 860160 1966080 4456448 10027008 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A001788 | 1 6 24 80 240 672 1792 4608 11520 28160 67584 159744 372736 860160 1966080 4456448 10027008 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | A003418 | 1 2 6 12 60 60 420 840 2520 2520 27720 27720 360360 360360 360360 720720 12252240 12252240 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 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 |
| Std | RowMaxMax k=0..n | T(n, k) | | A100071 | 1 2 6 12 30 60 140 280 630 1260 2772 5544 12012 24024 51480 102960 218790 437580 923780 1847560 |
| Std | ColMiddleT(n, n // 2) | A100071 | 1 2 6 12 30 60 140 280 630 1260 2772 5544 12012 24024 51480 102960 218790 437580 923780 1847560 |
| Std | CentralET(2 n, n) | A002457 | 1 6 30 140 630 2772 12012 51480 218790 923780 3879876 16224936 67603900 280816200 1163381400 |
| Std | CentralOT(2 n + 1, n) | A005430 | 2 12 60 280 1260 5544 24024 102960 437580 1847560 7759752 32449872 135207800 561632400 2326762800 |
| Std | ColLeftT(n, 0) | 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 | ColRightT(n, 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 | BinConv∑ k=0..n C(n, k) T(n, k) | A037965 | 1 4 18 80 350 1512 6468 27456 115830 486200 2032316 8465184 35154028 145608400 601749000 2481880320 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A002457 | 1 0 -6 0 30 0 -140 0 630 0 -2772 0 12012 0 -51480 0 218790 0 -923780 0 3879876 0 -16224936 0 |
| Std | TransNat0∑ k=0..n T(n, k) k | A001815 | 0 2 12 48 160 480 1344 3584 9216 23040 56320 135168 319488 745472 1720320 3932160 8912896 20054016 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A001788 | 1 6 24 80 240 672 1792 4608 11520 28160 67584 159744 372736 860160 1966080 4456448 10027008 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 2 18 96 400 1440 4704 14336 41472 115200 309760 811008 2076672 5218304 12902400 31457280 75759616 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A027471 | 1 6 27 108 405 1458 5103 17496 59049 196830 649539 2125764 6908733 22320522 71744535 229582512 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^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 |
| Std | DiagRow1T(n + 1, n) | A002378 | 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 | DiagRow2T(n + 2, n) | A027480 | 3 12 30 60 105 168 252 360 495 660 858 1092 1365 1680 2040 2448 2907 3420 3990 4620 5313 6072 6900 |
| Std | DiagRow3T(n + 3, n) | A033488 | 4 20 60 140 280 504 840 1320 1980 2860 4004 5460 7280 9520 12240 15504 19380 23940 29260 35420 |
| Std | DiagCol1T(n + 1, 1) | A002378 | 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 | DiagCol2T(n + 2, 2) | A027480 | 3 12 30 60 105 168 252 360 495 660 858 1092 1365 1680 2040 2448 2907 3420 3990 4620 5313 6072 6900 |
| Std | DiagCol3T(n + 3, 3) | A033488 | 4 20 60 140 280 504 840 1320 1980 2860 4004 5460 7280 9520 12240 15504 19380 23940 29260 35420 |
| Std | Polysee docs | A104002 | 1 2 1 3 4 1 4 12 6 1 5 32 27 8 1 6 80 108 48 10 1 7 192 405 256 75 12 1 8 448 1458 1280 500 108 14 |
| Std | PolyRow1∑ k=0..1 T(1, k) n^k | A005843 | 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 |
| Std | PolyRow2∑ k=0..2 T(2, k) n^k | A033428 | 3 12 27 48 75 108 147 192 243 300 363 432 507 588 675 768 867 972 1083 1200 1323 1452 1587 1728 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | A033430 | 4 32 108 256 500 864 1372 2048 2916 4000 5324 6912 8788 10976 13500 16384 19652 23328 27436 32000 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A027471 | 1 6 27 108 405 1458 5103 17496 59049 196830 649539 2125764 6908733 22320522 71744535 229582512 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A002697 | 1 8 48 256 1280 6144 28672 131072 589824 2621440 11534336 50331648 218103808 939524096 4026531840 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A000312 | 1 4 27 256 3125 46656 823543 16777216 387420489 10000000000 285311670611 8916100448256 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A003506 | 1 2 -2 3 -6 3 4 -12 12 -4 5 -20 30 -20 5 6 -30 60 -60 30 -6 7 -42 105 -140 105 -42 7 8 -56 168 -280 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A003506 | 1 -2 2 3 -6 3 -4 12 -12 4 5 -20 30 -20 5 -6 30 -60 60 -30 6 7 -42 105 -140 105 -42 7 -8 56 -168 280 |
| Alt | Accsee docs | missing | 1 2 0 3 -3 0 4 -8 4 0 5 -15 15 -5 0 6 -24 36 -24 6 0 7 -35 70 -70 35 -7 0 8 -48 120 -160 120 -48 8 |
| Alt | AccRevsee docs | missing | 1 -2 0 3 -3 0 -4 8 -4 0 5 -15 15 -5 0 -6 24 -36 24 -6 0 7 -35 70 -70 35 -7 0 -8 48 -120 160 -120 48 |
| Alt | AntiDiagsee docs | A128502 | 1 2 3 -2 4 -6 5 -12 3 6 -20 12 7 -30 30 -4 8 -42 60 -20 9 -56 105 -60 5 10 -72 168 -140 30 11 -90 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 2 -4 3 -12 9 4 -24 36 -16 5 -40 90 -80 25 6 -60 180 -240 150 -36 7 -84 315 -560 525 -252 49 8 |
| Alt | 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 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A057711 | 1 2 6 16 40 96 224 512 1152 2560 5632 12288 26624 57344 122880 262144 557056 1179648 2490368 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A057711 | 0 -2 -6 -16 -40 -96 -224 -512 -1152 -2560 -5632 -12288 -26624 -57344 -122880 -262144 -557056 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A001787 | 1 4 12 32 80 192 448 1024 2304 5120 11264 24576 53248 114688 245760 524288 1114112 2359296 4980736 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A001787 | 1 4 12 32 80 192 448 1024 2304 5120 11264 24576 53248 114688 245760 524288 1114112 2359296 4980736 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A186731 | 1 2 1 -2 -4 -2 3 6 3 -4 -8 -4 5 10 5 -6 -12 -6 7 14 7 -8 -16 -8 9 18 9 -10 -20 -10 11 22 11 -12 -24 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A130706 | 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 0 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A130706 | 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 0 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | A003418 | 1 2 6 12 60 60 420 840 2520 2520 27720 27720 360360 360360 360360 720720 12252240 12252240 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 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 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A100071 | 1 2 6 12 30 60 140 280 630 1260 2772 5544 12012 24024 51480 102960 218790 437580 923780 1847560 |
| Alt | ColMiddleT(n, n // 2) | A100071 | 1 2 -6 -12 30 60 -140 -280 630 1260 -2772 -5544 12012 24024 -51480 -102960 218790 437580 -923780 |
| Alt | CentralET(2 n, n) | A002457 | 1 -6 30 -140 630 -2772 12012 -51480 218790 -923780 3879876 -16224936 67603900 -280816200 1163381400 |
| Alt | CentralOT(2 n + 1, n) | A005430 | 2 -12 60 -280 1260 -5544 24024 -102960 437580 -1847560 7759752 -32449872 135207800 -561632400 |
| Alt | ColLeftT(n, 0) | 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 |
| Alt | ColRightT(n, 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 | BinConv∑ k=0..n C(n, k) T(n, k) | A002457 | 1 0 -6 0 30 0 -140 0 630 0 -2772 0 12012 0 -51480 0 218790 0 -923780 0 3879876 0 -16224936 0 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A037965 | 1 -4 18 -80 350 -1512 6468 -27456 115830 -486200 2032316 -8465184 35154028 -145608400 601749000 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A335462 | 0 -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 0 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A130706 | 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 0 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -2 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^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 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A027471 | 1 -6 27 -108 405 -1458 5103 -17496 59049 -196830 649539 -2125764 6908733 -22320522 71744535 |
| Alt | DiagRow1T(n + 1, n) | A002378 | 2 -6 12 -20 30 -42 56 -72 90 -110 132 -156 182 -210 240 -272 306 -342 380 -420 462 -506 552 -600 |
| Alt | DiagRow2T(n + 2, n) | A027480 | 3 -12 30 -60 105 -168 252 -360 495 -660 858 -1092 1365 -1680 2040 -2448 2907 -3420 3990 -4620 5313 |
| Alt | DiagRow3T(n + 3, n) | A033488 | 4 -20 60 -140 280 -504 840 -1320 1980 -2860 4004 -5460 7280 -9520 12240 -15504 19380 -23940 29260 |
| Alt | DiagCol1T(n + 1, 1) | A002378 | -2 -6 -12 -20 -30 -42 -56 -72 -90 -110 -132 -156 -182 -210 -240 -272 -306 -342 -380 -420 -462 -506 |
| Alt | DiagCol2T(n + 2, 2) | A027480 | 3 12 30 60 105 168 252 360 495 660 858 1092 1365 1680 2040 2448 2907 3420 3990 4620 5313 6072 6900 |
| Alt | DiagCol3T(n + 3, 3) | A033488 | -4 -20 -60 -140 -280 -504 -840 -1320 -1980 -2860 -4004 -5460 -7280 -9520 -12240 -15504 -19380 |
| Alt | Polysee docs | missing | 1 2 1 3 0 1 4 0 -2 1 5 0 3 -4 1 6 0 -4 12 -6 1 7 0 5 -32 27 -8 1 8 0 -6 80 -108 48 -10 1 9 0 7 -192 |
| Alt | PolyRow1∑ k=0..1 T(1, k) n^k | A005843 | 2 0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -28 -30 -32 -34 -36 -38 -40 -42 -44 -46 -48 -50 |
| Alt | PolyRow2∑ k=0..2 T(2, k) n^k | A033428 | 3 0 3 12 27 48 75 108 147 192 243 300 363 432 507 588 675 768 867 972 1083 1200 1323 1452 1587 1728 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | A033430 | 4 0 -4 -32 -108 -256 -500 -864 -1372 -2048 -2916 -4000 -5324 -6912 -8788 -10976 -13500 -16384 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^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 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A001787 | 1 -4 12 -32 80 -192 448 -1024 2304 -5120 11264 -24576 53248 -114688 245760 -524288 1114112 -2359296 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 3 -32 405 -6144 109375 -2239488 51883209 -1342177280 38354628411 -1200000000000 40799568897373 |
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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.