OEIS Similars: A358694, A109822
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A358694 | 1 0 1 0 2 1 0 6 4 1 0 24 18 7 1 0 120 96 46 11 1 0 720 600 326 101 16 1 0 5040 4320 2556 932 197 22 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 2 0 1 4 6 0 1 7 18 24 0 1 11 46 96 120 0 1 16 101 326 600 720 0 1 22 197 932 2556 4320 5040 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A227341 | 1 0 1 0 -2 1 0 2 -4 1 0 -2 10 -7 1 0 2 -22 31 -11 1 0 -2 46 -115 75 -16 1 0 2 -94 391 -415 155 -22 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -2 0 1 -4 2 0 1 -7 10 -2 0 1 -11 31 -22 2 0 1 -16 75 -115 46 -2 0 1 -22 155 -415 391 -94 2 |
| Std | Accsee docs | missing | 1 0 1 0 2 3 0 6 10 11 0 24 42 49 50 0 120 216 262 273 274 0 720 1320 1646 1747 1763 1764 0 5040 |
| Std | AccRevsee docs | missing | 1 1 1 1 3 3 1 5 11 11 1 8 26 50 50 1 12 58 154 274 274 1 17 118 444 1044 1764 1764 1 23 220 1152 |
| Std | AntiDiagsee docs | missing | 1 0 0 1 0 2 0 6 1 0 24 4 0 120 18 1 0 720 96 7 0 5040 600 46 1 0 40320 4320 326 11 0 362880 35280 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 4 3 0 12 12 4 0 48 54 28 5 0 240 288 184 55 6 0 1440 1800 1304 505 96 7 0 10080 12960 10224 |
| Std | RowSum∑ k=0..n T(n, k) | A000254 | 1 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A182541 | 1 0 1 4 19 107 702 5274 44712 422568 4407120 50292720 623471040 8344624320 119938250880 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 2 7 31 167 1062 7794 64872 604008 6221520 70251120 862971840 11458134720 163527396480 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A001710 | 1 -1 -1 -3 -12 -60 -360 -2520 -20160 -181440 -1814400 -19958400 -239500800 -3113510400 -43589145600 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000254 | 1 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 1 2 7 28 139 823 5687 44977 400818 3974520 43404974 517626129 6692859524 93258105256 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 5 27 165 1145 8960 78344 758548 8066484 93532824 1175064264 15905755008 230839150464 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 7 28 135 773 5152 39268 337292 3225852 34010856 392005656 4904445312 66202235136 959088092544 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 12 504 121440 59266800 1084064113440 103321840810930560 6456945582111373908894720 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A174965 | 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 1 1 |
| Std | RowMaxMax k=0..n | T(n, k) | | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Std | ColMiddleT(n, n // 2) | missing | 1 0 2 6 18 96 326 2556 9080 94852 342964 4496284 16369178 258795044 944218666 17499398776 |
| Std | CentralET(2 n, n) | missing | 1 2 18 326 9080 342964 16369178 944218666 63850536496 4951400140040 433031885253418 |
| Std | CentralOT(2 n + 1, n) | missing | 0 6 96 2556 94852 4496284 258795044 17499398776 1358262331112 118948447958696 11597528345789328 |
| 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) | missing | 1 1 5 31 233 2076 21452 252372 3329349 48644302 779147639 13565379433 254899449136 5138081438816 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 -3 7 -15 46 -420 5384 -62811 656620 -6213537 52114085 -354833336 1339350000 8402462848 |
| Std | TransNat0∑ k=0..n T(n, k) k | A081052 | 0 1 4 17 85 499 3388 26200 227708 2199276 23382216 271461816 3418002432 46399476096 675622445184 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 7 28 135 773 5152 39268 337292 3225852 34010856 392005656 4904445312 66202235136 959088092544 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 6 31 175 1119 8106 66002 598524 5992036 65708368 783813920 10109151312 140220416400 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A129890 | 1 1 5 33 279 2895 35685 509985 8294895 151335135 3061162125 68000295825 1645756410375 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A192459 | 1 1 -3 17 -133 1315 -15675 218505 -3485685 62607195 -1250116875 27468111825 -658579954725 |
| Std | DiagRow1T(n + 1, n) | A000124 | 0 2 4 7 11 16 22 29 37 46 56 67 79 92 106 121 137 154 172 191 211 232 254 277 301 326 352 379 407 |
| Std | DiagRow2T(n + 2, n) | A308305 | 0 6 18 46 101 197 351 583 916 1376 1992 2796 3823 5111 6701 8637 10966 13738 17006 20826 25257 |
| Std | DiagRow3T(n + 3, n) | missing | 0 24 96 326 932 2311 5119 10366 19526 34662 58566 94914 148436 225101 332317 479146 676534 937556 |
| Std | DiagCol1T(n + 1, 1) | A000142 | 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 |
| Std | DiagCol2T(n + 2, 2) | A001563 | 1 4 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800 |
| Std | DiagCol3T(n + 3, 3) | A067318 | 1 7 46 326 2556 22212 212976 2239344 25659360 318540960 4261576320 61148511360 937030429440 |
| Std | Polysee docs | missing | 1 0 1 0 1 1 0 3 2 1 0 11 8 3 1 0 50 36 15 4 1 0 274 192 81 24 5 1 0 1764 1200 504 152 35 6 1 0 |
| 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 | A005563 | 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728 783 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 11 36 81 152 255 396 581 816 1107 1460 1881 2376 2951 3612 4365 5216 6171 7236 8417 9720 11151 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A052582 | 1 2 8 36 192 1200 8640 70560 645120 6531840 72576000 878169600 11496038400 161902540800 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 15 81 504 3600 29160 264600 2661120 29393280 353808000 4610390400 64665216000 971415244800 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 8 81 1088 18750 398304 10084200 296478720 9923906160 372464064000 15487179523200 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A358694 | 1 0 -1 0 -2 1 0 -6 4 -1 0 -24 18 -7 1 0 -120 96 -46 11 -1 0 -720 600 -326 101 -16 1 0 -5040 4320 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 -1 0 1 -2 0 -1 4 -6 0 1 -7 18 -24 0 -1 11 -46 96 -120 0 1 -16 101 -326 600 -720 0 -1 22 -197 932 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 0 1 0 2 1 0 -2 -4 1 0 -26 -46 7 1 0 122 226 -31 -11 1 0 3446 6358 -877 -277 16 1 0 -36258 -67026 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 2 0 1 -4 -2 0 1 7 -46 -26 0 1 -11 -31 226 122 0 1 16 -277 -877 6358 3446 0 1 -22 -155 2995 |
| Alt | Accsee docs | missing | 1 0 -1 0 -2 -1 0 -6 -2 -3 0 -24 -6 -13 -12 0 -120 -24 -70 -59 -60 0 -720 -120 -446 -345 -361 -360 0 |
| Alt | AccRevsee docs | missing | 1 -1 -1 1 -1 -1 -1 3 -3 -3 1 -6 12 -12 -12 -1 10 -36 60 -60 -60 1 -15 86 -240 360 -360 -360 -1 21 |
| Alt | AntiDiagsee docs | missing | 1 0 0 -1 0 -2 0 -6 1 0 -24 4 0 -120 18 -1 0 -720 96 -7 0 -5040 600 -46 1 0 -40320 4320 -326 11 0 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 0 -2 0 -4 3 0 -12 12 -4 0 -48 54 -28 5 0 -240 288 -184 55 -6 0 -1440 1800 -1304 505 -96 7 0 |
| Alt | RowSum∑ k=0..n T(n, k) | A001710 | 1 -1 -1 -3 -12 -60 -360 -2520 -20160 -181440 -1814400 -19958400 -239500800 -3113510400 -43589145600 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A182541 | 1 0 1 4 19 107 702 5274 44712 422568 4407120 50292720 623471040 8344624320 119938250880 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -2 -7 -31 -167 -1062 -7794 -64872 -604008 -6221520 -70251120 -862971840 -11458134720 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000254 | 1 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000254 | 1 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 0 -1 -2 -5 -20 -103 -631 -4485 -36315 -330056 -3327536 -36854972 -444860381 -5812555934 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -3 -11 -55 -333 -2352 -18960 -171720 -1726200 -19071360 -229703040 -2995574400 -42052348800 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -2 -1 -4 -17 -87 -528 -3720 -29880 -269640 -2701440 -29756160 -357436800 -4650307200 -65144217600 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 12 504 121440 59266800 1084064113440 103321840810930560 6456945582111373908894720 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A174965 | 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 1 1 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 0 -2 -6 18 96 -326 -2556 9080 94852 -342964 -4496284 16369178 258795044 -944218666 -17499398776 |
| Alt | CentralET(2 n, n) | missing | 1 -2 18 -326 9080 -342964 16369178 -944218666 63850536496 -4951400140040 433031885253418 |
| Alt | CentralOT(2 n + 1, n) | missing | 0 -6 96 -2556 94852 -4496284 258795044 -17499398776 1358262331112 -118948447958696 |
| 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 -3 -7 -15 -46 -420 -5384 -62811 -656620 -6213537 -52114085 -354833336 -1339350000 8402462848 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 5 -31 233 -2076 21452 -252372 3329349 -48644302 779147639 -13565379433 254899449136 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A138772 | 0 -1 0 -1 -5 -27 -168 -1200 -9720 -88200 -887040 -9797760 -117936000 -1536796800 -21555072000 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -2 -1 -4 -17 -87 -528 -3720 -29880 -269640 -2701440 -29756160 -357436800 -4650307200 -65144217600 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | A323618 | 0 -1 2 1 1 1 -2 -34 -324 -2988 -28944 -300816 -3371040 -40710240 -528439680 -7348717440 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A192459 | 1 -1 -3 -17 -133 -1315 -15675 -218505 -3485685 -62607195 -1250116875 -27468111825 -658579954725 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A129890 | 1 -1 5 -33 279 -2895 35685 -509985 8294895 -151335135 3061162125 -68000295825 1645756410375 |
| Alt | DiagRow1T(n + 1, n) | A000124 | 0 -2 4 -7 11 -16 22 -29 37 -46 56 -67 79 -92 106 -121 137 -154 172 -191 211 -232 254 -277 301 -326 |
| Alt | DiagRow2T(n + 2, n) | A308305 | 0 -6 18 -46 101 -197 351 -583 916 -1376 1992 -2796 3823 -5111 6701 -8637 10966 -13738 17006 -20826 |
| Alt | DiagRow3T(n + 3, n) | missing | 0 -24 96 -326 932 -2311 5119 -10366 19526 -34662 58566 -94914 148436 -225101 332317 -479146 676534 |
| Alt | DiagCol1T(n + 1, 1) | A000142 | -1 -2 -6 -24 -120 -720 -5040 -40320 -362880 -3628800 -39916800 -479001600 -6227020800 -87178291200 |
| Alt | DiagCol2T(n + 2, 2) | A001563 | 1 4 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800 |
| Alt | DiagCol3T(n + 3, 3) | A067318 | -1 -7 -46 -326 -2556 -22212 -212976 -2239344 -25659360 -318540960 -4261576320 -61148511360 |
| Alt | Polysee docs | missing | 1 0 1 0 -1 1 0 -1 -2 1 0 -3 0 -3 1 0 -12 -4 3 -4 1 0 -60 -16 -9 8 -5 1 0 -360 -80 -18 -24 15 -6 1 0 |
| 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 | A005563 | 0 -1 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 -3 -4 -9 -24 -55 -108 -189 -304 -459 -660 -913 -1224 -1599 -2044 -2565 -3168 -3859 -4644 -5529 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -2 0 -4 -16 -80 -480 -3360 -26880 -241920 -2419200 -26611200 -319334400 -4151347200 -58118860800 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -3 3 -9 -18 -90 -540 -3780 -30240 -272160 -2721600 -29937600 -359251200 -4670265600 -65383718400 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 -1 0 -9 0 -200 0 -8820 0 -653184 0 -73180800 0 -11564467200 0 -2451889440000 0 -671854030848000 0 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 0 1 2 0 1 4 6 0 1 7 18 24 0 1 11 46 96 120 0 1 16 101 326 600 720 0 1 22 197 932 2556 4320 5040 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A227341 | 1 0 1 0 -2 1 0 2 -4 1 0 -2 10 -7 1 0 2 -22 31 -11 1 0 -2 46 -115 75 -16 1 0 2 -94 391 -415 155 -22 |
| Rev | Accsee docs | missing | 1 1 1 1 3 3 1 5 11 11 1 8 26 50 50 1 12 58 154 274 274 1 17 118 444 1044 1764 1764 1 23 220 1152 |
| Rev | AccRevsee docs | missing | 1 0 1 0 2 3 0 6 10 11 0 24 42 49 50 0 120 216 262 273 274 0 720 1320 1646 1747 1763 1764 0 5040 |
| Rev | AntiDiagsee docs | missing | 1 1 1 0 1 2 1 4 0 1 7 6 1 11 18 0 1 16 46 24 1 22 101 96 0 1 29 197 326 120 1 37 351 932 600 0 1 46 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 4 0 1 8 18 0 1 14 54 96 0 1 22 138 384 600 0 1 32 303 1304 3000 4320 0 1 44 591 3728 12780 |
| Rev | RowSum∑ k=0..n T(n, k) | A000254 | 1 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 1 7 19 167 702 7794 44712 604008 4407120 70251120 623471040 11458134720 119938250880 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 2 4 31 107 1062 5274 64872 422568 6221520 50292720 862971840 8344624320 163527396480 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A001710 | 1 1 -1 3 -12 60 -360 2520 -20160 181440 -1814400 19958400 -239500800 3113510400 -43589145600 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000254 | 1 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 3 5 14 30 87 220 673 1921 6217 19492 66630 225369 811110 2923139 11036327 42000207 165749078 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 7 28 135 773 5152 39268 337292 3225852 34010856 392005656 4904445312 66202235136 959088092544 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 5 27 165 1145 8960 78344 758548 8066484 93532824 1175064264 15905755008 230839150464 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 12 504 121440 59266800 1084064113440 103321840810930560 6456945582111373908894720 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A174965 | 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 1 1 |
| Rev | RowMaxMax k=0..n | T(n, k) | | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 2 4 18 46 326 932 9080 27568 342964 1079354 16369178 52724894 944218666 3090075848 63850536496 |
| Rev | CentralET(2 n, n) | missing | 1 2 18 326 9080 342964 16369178 944218666 63850536496 4951400140040 433031885253418 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 4 46 932 27568 1079354 52724894 3090075848 211361047584 16530707226038 1455228480277878 |
| 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) | missing | 1 1 5 31 233 2076 21452 252372 3329349 48644302 779147639 13565379433 254899449136 5138081438816 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 -3 -7 -15 -46 -420 -5384 -62811 -656620 -6213537 -52114085 -354833336 -1339350000 8402462848 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 2 16 115 871 7196 65276 648964 7039908 82904184 1054520424 14419312128 211036391424 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 5 27 165 1145 8960 78344 758548 8066484 93532824 1175064264 15905755008 230839150464 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 2 28 295 2979 30954 339534 3968572 49557724 660928048 9397458608 142124867664 2280500315664 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A052582 | 1 2 8 36 192 1200 8640 70560 645120 6531840 72576000 878169600 11496038400 161902540800 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 0 -4 -16 -80 -480 -3360 -26880 -241920 -2419200 -26611200 -319334400 -4151347200 -58118860800 |
| Rev | DiagRow1T(n + 1, n) | A000142 | 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 |
| Rev | DiagRow2T(n + 2, n) | A001563 | 1 4 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800 |
| Rev | DiagRow3T(n + 3, n) | A067318 | 1 7 46 326 2556 22212 212976 2239344 25659360 318540960 4261576320 61148511360 937030429440 |
| Rev | DiagCol1T(n + 1, 1) | A000124 | 0 2 4 7 11 16 22 29 37 46 56 67 79 92 106 121 137 154 172 191 211 232 254 277 301 326 352 379 407 |
| Rev | DiagCol2T(n + 2, 2) | A308305 | 0 6 18 46 101 197 351 583 916 1376 1992 2796 3823 5111 6701 8637 10966 13738 17006 20826 25257 |
| Rev | DiagCol3T(n + 3, 3) | missing | 0 24 96 326 932 2311 5119 10366 19526 34662 58566 94914 148436 225101 332317 479146 676534 937556 |
| Rev | Polysee docs | missing | 1 1 1 1 1 1 1 3 1 1 1 11 5 1 1 1 50 33 7 1 1 1 274 279 67 9 1 1 1 1764 2895 832 113 11 1 1 1 13068 |
| 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 | A005408 | 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A080859 | 1 11 33 67 113 171 241 323 417 523 641 771 913 1067 1233 1411 1601 1803 2017 2243 2481 2731 2993 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A129890 | 1 1 5 33 279 2895 35685 509985 8294895 151335135 3061162125 68000295825 1645756410375 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 7 67 832 12760 233320 4957960 120097600 3266979520 98617993600 3271434812800 118299925004800 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 5 67 1853 88206 6450469 672023640 94571849385 17282558344240 3978887127248061 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A227341 | 1 0 1 0 -2 1 0 2 -4 1 0 -2 10 -7 1 0 2 -22 31 -11 1 0 -2 46 -115 75 -16 1 0 2 -94 391 -415 155 -22 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 -2 0 1 -4 2 0 1 -7 10 -2 0 1 -11 31 -22 2 0 1 -16 75 -115 46 -2 0 1 -22 155 -415 391 -94 2 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 0 1 2 0 1 4 6 0 1 7 18 24 0 1 11 46 96 120 0 1 16 101 326 600 720 0 1 22 197 932 2556 4320 5040 |
| Inv | Accsee docs | missing | 1 0 1 0 -2 -1 0 2 -2 -1 0 -2 8 1 2 0 2 -20 11 0 1 0 -2 44 -71 4 -12 -11 0 2 -92 299 -116 39 17 18 0 |
| Inv | AccRevsee docs | missing | 1 1 1 1 -1 -1 1 -3 -1 -1 1 -6 4 2 2 1 -10 21 -1 1 1 1 -15 60 -55 -9 -11 -11 1 -21 134 -281 110 16 |
| Inv | AntiDiagsee docs | missing | 1 0 0 1 0 -2 0 2 1 0 -2 -4 0 2 10 1 0 -2 -22 -7 0 2 46 31 1 0 -2 -94 -115 -11 0 2 190 391 75 1 0 -2 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 0 2 0 -4 3 0 4 -12 4 0 -4 30 -28 5 0 4 -66 124 -55 6 0 -4 138 -460 375 -96 7 0 4 -282 1564 -2075 |
| Inv | RowSum∑ k=0..n T(n, k) | A101851 | 1 1 -1 -1 2 1 -11 18 41 -317 680 1767 -19911 68264 59643 -2076973 11905466 -18577387 -269836343 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 0 1 -4 11 -33 122 -531 2529 -12802 68901 -396389 2436128 -15894885 109301701 -787967420 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -2 3 -9 34 -133 549 -2488 12485 -68221 398156 -2456039 15963149 -109242058 785890447 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A011968 | 1 -1 3 -7 20 -67 255 -1080 5017 -25287 137122 -794545 4892167 -31858034 218543759 -1573857867 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A011968 | 1 1 3 7 20 67 255 1080 5017 25287 137122 794545 4892167 31858034 218543759 1573857867 11863100692 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A363071 | 1 0 1 -2 3 -6 13 -31 80 -222 659 -2082 6966 -24574 91067 -353443 1432909 -6054025 26599192 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -3 -1 9 -6 -48 167 11 -2173 8567 -474 -170668 947075 -1241971 -19249129 171910069 -585651922 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 2 -1 -4 3 13 -40 -5 399 -1314 -407 23445 -108086 76885 2196259 -16059412 42388319 232681569 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 4 70 682 27600 5201242310 1425701518570 113987086706132640 154582298323624935907500 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A174965 | 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 1 1 |
| Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 4 10 31 115 415 2051 9471 49476 289255 1626130 10644964 72757685 484129646 3690623937 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 0 -2 2 10 -22 -115 391 2051 -9471 -49476 289255 1503139 -10644964 -55044704 458070613 2358391893 |
| Inv | CentralET(2 n, n) | missing | 1 -2 10 -115 2051 -49476 1503139 -55044704 2358391893 -115704218058 6394881998440 -393109352559287 |
| Inv | CentralOT(2 n + 1, n) | missing | 0 2 -22 391 -9471 289255 -10644964 458070613 -22557759081 1250790022560 -77104717255930 |
| 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 -3 -5 25 46 -592 302 19087 -91010 -499151 8009904 -17274237 -480679224 5143792457 2212589415 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 5 19 97 596 4224 33608 294767 2813068 28924993 317990212 3714589091 45872167706 596310326993 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 0 -3 1 12 -29 -23 358 -997 -1087 21678 -88175 8621 2136616 -13982439 30482853 251258956 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 2 -1 -4 3 13 -40 -5 399 -1314 -407 23445 -108086 76885 2196259 -16059412 42388319 232681569 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 2 -5 -9 42 -17 -363 1396 -227 -22085 111620 -116707 -2059731 16178698 -46542265 -208870637 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 -3 1 11 -41 21 633 -4253 10575 70285 -1060271 6587995 -7206553 -353104795 4799644809 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 1 5 17 71 355 2053 13377 96503 761251 6503333 59703825 585296775 6094959299 67119902949 |
| Inv | DiagRow1T(n + 1, n) | A000124 | 0 -2 -4 -7 -11 -16 -22 -29 -37 -46 -56 -67 -79 -92 -106 -121 -137 -154 -172 -191 -211 -232 -254 |
| Inv | DiagRow2T(n + 2, n) | A090809 | 0 2 10 31 75 155 287 490 786 1200 1760 2497 3445 4641 6125 7940 10132 12750 15846 19475 23695 28567 |
| Inv | DiagRow3T(n + 3, n) | missing | 0 -2 -22 -115 -415 -1190 -2912 -6342 -12630 -23430 -41030 -68497 -109837 -170170 -255920 -375020 |
| Inv | DiagCol1T(n + 1, 1) | A055642 | 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 |
| Inv | DiagCol2T(n + 2, 2) | A033484 | 1 -4 10 -22 46 -94 190 -382 766 -1534 3070 -6142 12286 -24574 49150 -98302 196606 -393214 786430 |
| Inv | DiagCol3T(n + 3, 3) | A091344 | 1 -7 31 -115 391 -1267 3991 -12355 37831 -115027 348151 -1050595 3164071 -9516787 28599511 |
| Inv | Polysee docs | missing | 1 0 1 0 1 1 0 -1 2 1 0 -1 0 3 1 0 2 -4 3 4 1 0 1 -4 -3 8 5 1 0 -11 20 -24 8 15 6 1 0 18 12 -3 -40 |
| 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 | A005563 | 0 -1 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 0 -1 -4 -3 8 35 84 161 272 423 620 869 1176 1547 1988 2505 3104 3791 4572 5453 6440 7539 8756 10097 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 2 0 -4 -4 20 12 -204 268 2292 -11828 -4300 300940 -1285772 -2689204 59952564 -264710900 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 3 3 -3 -24 -3 219 -84 -3183 7125 52950 -334857 -419685 12959106 -42123345 -341865687 3882755064 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 0 -3 -40 -415 -3756 -26544 -34448 3980763 111871580 2100756647 28045662600 108169803716 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 0 1 -2 0 1 -4 2 0 1 -7 10 -2 0 1 -11 31 -22 2 0 1 -16 75 -115 46 -2 0 1 -22 155 -415 391 -94 2 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A227341 | 1 0 1 0 -2 1 0 2 -4 1 0 -2 10 -7 1 0 2 -22 31 -11 1 0 -2 46 -115 75 -16 1 0 2 -94 391 -415 155 -22 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A358694 | 1 0 1 0 2 1 0 6 4 1 0 24 18 7 1 0 120 96 46 11 1 0 720 600 326 101 16 1 0 5040 4320 2556 932 197 22 |
| Inv:Rev | Accsee docs | missing | 1 1 1 1 -1 -1 1 -3 -1 -1 1 -6 4 2 2 1 -10 21 -1 1 1 1 -15 60 -55 -9 -11 -11 1 -21 134 -281 110 16 |
| Inv:Rev | AccRevsee docs | missing | 1 0 1 0 -2 -1 0 2 -2 -1 0 -2 8 1 2 0 2 -20 11 0 1 0 -2 44 -71 4 -12 -11 0 2 -92 299 -116 39 17 18 0 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 0 1 -2 1 -4 0 1 -7 2 1 -11 10 0 1 -16 31 -2 1 -22 75 -22 0 1 -29 155 -115 2 1 -37 287 -415 46 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 0 1 -4 0 1 -8 6 0 1 -14 30 -8 0 1 -22 93 -88 10 0 1 -32 225 -460 230 -12 0 1 -44 465 -1660 1955 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A101851 | 1 1 -1 -1 2 1 -11 18 41 -317 680 1767 -19911 68264 59643 -2076973 11905466 -18577387 -269836343 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 1 3 11 34 122 549 2529 12485 68901 398156 2436128 15963149 109301701 785890447 5937503079 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 0 -2 -4 -9 -33 -133 -531 -2488 -12802 -68221 -396389 -2456039 -15894885 -109242058 -787967420 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A011968 | 1 1 3 7 20 67 255 1080 5017 25287 137122 794545 4892167 31858034 218543759 1573857867 11863100692 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A011968 | 1 1 3 7 20 67 255 1080 5017 25287 137122 794545 4892167 31858034 218543759 1573857867 11863100692 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 1 -1 -3 -4 0 14 32 14 -118 -356 -224 1528 5244 3356 -27604 -96680 -46360 643048 2124912 288744 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 2 -1 -4 3 13 -40 -5 399 -1314 -407 23445 -108086 76885 2196259 -16059412 42388319 232681569 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -3 -1 9 -6 -48 167 11 -2173 8567 -474 -170668 947075 -1241971 -19249129 171910069 -585651922 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 4 70 682 27600 5201242310 1425701518570 113987086706132640 154582298323624935907500 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A174965 | 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 1 1 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 4 10 31 115 415 2051 9471 49476 289255 1626130 10644964 72757685 484129646 3690623937 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -2 -4 10 31 -115 -415 2051 8001 -49476 -202314 1503139 6342820 -55044704 -237540160 2358391893 |
| Inv:Rev | CentralET(2 n, n) | missing | 1 -2 10 -115 2051 -49476 1503139 -55044704 2358391893 -115704218058 6394881998440 -393109352559287 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -4 31 -415 8001 -202314 6342820 -237540160 10349606553 -514409197588 28727694118487 |
| 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 -3 -5 25 46 -592 302 19087 -91010 -499151 8009904 -17274237 -480679224 5143792457 2212589415 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 5 -19 97 -596 4224 -33608 294767 -2813068 28924993 -317990212 3714589091 -45872167706 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 0 -2 0 7 -7 -37 149 -30 -1856 7887 -2241 -150757 878811 -1301614 -17172156 160004603 -567074535 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -3 -1 9 -6 -48 167 11 -2173 8567 -474 -170668 947075 -1241971 -19249129 171910069 -585651922 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 0 -2 4 15 -53 -65 841 -1708 -7958 67655 -151489 -867691 9252739 -31956522 -94388020 1863477363 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 2 0 -4 -4 20 12 -204 268 2292 -11828 -4300 300940 -1285772 -2689204 59952564 -264710900 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -2 8 -28 116 -548 2884 -16644 104132 -700100 5022980 -38240772 307474500 -2600627524 23059485060 |
| Inv:Rev | DiagRow1T(n + 1, n) | A055642 | 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 |
| Inv:Rev | DiagRow2T(n + 2, n) | A033484 | 1 -4 10 -22 46 -94 190 -382 766 -1534 3070 -6142 12286 -24574 49150 -98302 196606 -393214 786430 |
| Inv:Rev | DiagRow3T(n + 3, n) | A091344 | 1 -7 31 -115 391 -1267 3991 -12355 37831 -115027 348151 -1050595 3164071 -9516787 28599511 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A000124 | 0 -2 -4 -7 -11 -16 -22 -29 -37 -46 -56 -67 -79 -92 -106 -121 -137 -154 -172 -191 -211 -232 -254 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A090809 | 0 2 10 31 75 155 287 490 786 1200 1760 2497 3445 4641 6125 7940 10132 12750 15846 19475 23695 28567 |
| Inv:Rev | DiagCol3T(n + 3, 3) | missing | 0 -2 -22 -115 -415 -1190 -2912 -6342 -12630 -23430 -41030 -68497 -109837 -170170 -255920 -375020 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 1 1 1 -1 1 1 1 -1 -3 1 1 1 2 1 -5 1 1 1 1 11 7 -7 1 1 1 -11 -41 16 17 -9 1 1 1 18 21 -185 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 | A005408 | 1 -1 -3 -5 -7 -9 -11 -13 -15 -17 -19 -21 -23 -25 -27 -29 -31 -33 -35 -37 -39 -41 -43 -45 -47 -49 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A056220 | 1 -1 1 7 17 31 49 71 97 127 161 199 241 287 337 391 449 511 577 647 721 799 881 967 1057 1151 1249 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 -3 1 11 -41 21 633 -4253 10575 70285 -1060271 6587995 -7206553 -353104795 4799644809 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 -5 7 16 -185 763 412 -37247 359431 -1630802 -8175875 269835955 -3226480706 19332564439 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 1 -3 7 5 -779 21829 -540672 11905753 -128861693 -11774133859 1520185039957 -133257057306275 |
| << | 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.