SIERPINSKI[0] 1
[1] 1, 1
[2] 1, 0, 1
[3] 1, 1, 1, 1
[4] 1, 0, 0, 0, 1
[5] 1, 1, 0, 0, 1, 1

      OEIS Similars: A047999, A090971, A114700, A143200, A166282

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(n, k), 0 ≤ k ≤ nA0479991 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0
StdRevT(n, n - k), 0 ≤ k ≤ nA0479991 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0
StdInvT-1(n, k), 0 ≤ k ≤ nA0479991 -1 1 -1 0 1 1 -1 -1 1 -1 0 0 0 1 1 -1 0 0 -1 1 1 0 -1 0 -1 0 1 -1 1 1 -1 1 -1 -1 1 -1 0 0 0 0 0 0
StdRevInvT-1(n, n - k), 0 ≤ k ≤ nA0479991 1 -1 1 0 -1 1 -1 -1 1 1 0 0 0 -1 1 -1 0 0 -1 1 1 0 -1 0 -1 0 1 1 -1 -1 1 -1 1 1 -1 1 0 0 0 0 0 0
StdInvRev(T(n, n - k))-1, 0 ≤ k ≤ nA0479991 -1 1 -1 0 1 1 -1 -1 1 -1 0 0 0 1 1 -1 0 0 -1 1 1 0 -1 0 -1 0 1 -1 1 1 -1 1 -1 -1 1 -1 0 0 0 0 0 0
StdAccsee docsA2613631 1 2 1 1 2 1 2 3 4 1 1 1 1 2 1 2 2 2 3 4 1 1 2 2 3 3 4 1 2 3 4 5 6 7 8 1 1 1 1 1 1 1 1 2 1 2 2 2 2
StdAccRevsee docsA2613631 1 2 1 1 2 1 2 3 4 1 1 1 1 2 1 2 2 2 3 4 1 1 2 2 3 3 4 1 2 3 4 5 6 7 8 1 1 1 1 1 1 1 1 2 1 2 2 2 2
StdAntiDiagsee docsmissing1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1
StdDiffx1T(n, k) (k+1)missing1 1 2 1 0 3 1 2 3 4 1 0 0 0 5 1 2 0 0 5 6 1 0 3 0 5 0 7 1 2 3 4 5 6 7 8 1 0 0 0 0 0 0 0 9 1 2 0 0 0
StdRowSum∑ k=0..n T(n, k)A0013161 2 2 4 2 4 4 8 2 4 4 8 4 8 8 16 2 4 4 8 4 8 8 16 4 8 8 16 8 16 16 32 2 4 4 8 4 8 8 16 4 8 8 16 8
StdEvenSum∑ k=0..n T(n, k) even(k)A0606321 1 2 2 2 2 4 4 2 2 4 4 4 4 8 8 2 2 4 4 4 4 8 8 4 4 8 8 8 8 16 16 2 2 4 4 4 4 8 8 4 4 8 8 8 8 16 16
StdOddSum∑ k=0..n T(n, k) odd(k)A0013160 1 0 2 0 2 0 4 0 2 0 4 0 4 0 8 0 2 0 4 0 4 0 8 0 4 0 8 0 8 0 16 0 2 0 4 0 4 0 8 0 4 0 8 0 8 0 16
StdAltSum∑ k=0..n T(n, k) (-1)^kA0013161 0 2 0 2 0 4 0 2 0 4 0 4 0 8 0 2 0 4 0 4 0 8 0 4 0 8 0 8 0 16 0 2 0 4 0 4 0 8 0 4 0 8 0 8 0 16 0
StdAbsSum∑ k=0..n | T(n, k) |A0013161 2 2 4 2 4 4 8 2 4 4 8 4 8 8 16 2 4 4 8 4 8 8 16 4 8 8 16 8 16 16 32 2 4 4 8 4 8 8 16 4 8 8 16 8
StdDiagSum∑ k=0..n // 2 T(n - k, k)A0024871 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9
StdAccSum∑ k=0..n ∑ j=0..k T(n, j)missing1 3 4 10 6 14 16 36 10 22 24 52 28 60 64 136 18 38 40 84 44 92 96 200 52 108 112 232 120 248 256
StdAccRevSum∑ k=0..n ∑ j=0..k T(n, n - j)missing1 3 4 10 6 14 16 36 10 22 24 52 28 60 64 136 18 38 40 84 44 92 96 200 52 108 112 232 120 248 256
StdRowLcmLcm k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
StdRowGcdGcd k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
StdRowMaxMax k=0..n | T(n, k) |A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
StdColMiddleT(n, n // 2)A2092291 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
StdCentralET(2 n, n)A0000071 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
StdCentralOT(2 n + 1, n)A2092291 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
StdColLeftT(n, 0)A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
StdColRightT(n, n)A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
StdBinConv∑ k=0..n C(n, k) T(n, k)A0885601 2 2 8 2 12 32 128 2 20 92 464 992 4032 8192 32768 2 36 308 2320 9692 52712 164320 781312 1470944
StdInvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 0 2 0 2 0 32 0 2 0 92 0 992 0 8192 0 2 0 308 0 9692 0 164320 0 1470944 0 13748672 0 67100672 0
StdTransNat0∑ k=0..n T(n, k) kA3350630 1 2 6 4 10 12 28 8 18 20 44 24 52 56 120 16 34 36 76 40 84 88 184 48 100 104 216 112 232 240 496
StdTransNat1∑ k=0..n T(n, k) (k + 1)missing1 3 4 10 6 14 16 36 10 22 24 52 28 60 64 136 18 38 40 84 44 92 96 200 52 108 112 232 120 248 256
StdTransSqrs∑ k=0..n T(n, k) k^2missing0 1 4 14 16 42 56 140 64 146 168 380 224 500 560 1240 256 546 584 1244 672 1428 1520 3224 896 1892
StdPosHalf∑ k=0..n 2^n T(n, k) (1/2)^kA0013171 3 5 15 17 51 85 255 257 771 1285 3855 4369 13107 21845 65535 65537 196611 327685 983055 1114129
StdDiagRow1T(n + 1, n)A0000351 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
StdDiagRow2T(n + 2, n)A1338721 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0
StdDiagRow3T(n + 3, n)A1212621 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
StdDiagCol1T(n + 1, 1)A0000351 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
StdDiagCol2T(n + 2, 2)A1338721 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0
StdDiagCol3T(n + 3, 3)A1212621 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
StdPolysee docsmissing1 1 1 1 2 1 1 2 3 1 1 4 5 4 1 1 2 15 10 5 1 1 4 17 40 17 6 1 1 4 51 82 85 26 7 1 1 8 85 328 257 156
StdPolyRow1∑ k=0..1 T(1, k) n^kA0000271 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
StdPolyRow2∑ k=0..2 T(2, k) n^kA0025221 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730
StdPolyRow3∑ k=0..3 T(3, k) n^kA0536981 4 15 40 85 156 259 400 585 820 1111 1464 1885 2380 2955 3616 4369 5220 6175 7240 8421 9724 11155
StdPolyCol2∑ k=0..n T(n, k) 2^kA0013171 3 5 15 17 51 85 255 257 771 1285 3855 4369 13107 21845 65535 65537 196611 327685 983055 1114129
StdPolyCol3∑ k=0..n T(n, k) 3^kA1003071 4 10 40 82 328 820 3280 6562 26248 65620 262480 538084 2152336 5380840 21523360 43046722
StdPolyDiag∑ k=0..n T(n, k) n^kmissing1 2 5 40 257 3756 47989 960800 16777217 430467220 10100000101 313821403248 8916530450689
AltTriangleT(n, k), 0 ≤ k ≤ nA0479991 1 -1 1 0 1 1 -1 1 -1 1 0 0 0 1 1 -1 0 0 1 -1 1 0 1 0 1 0 1 1 -1 1 -1 1 -1 1 -1 1 0 0 0 0 0 0 0 1
AltRevT(n, n - k), 0 ≤ k ≤ nA0479991 -1 1 1 0 1 -1 1 -1 1 1 0 0 0 1 -1 1 0 0 -1 1 1 0 1 0 1 0 1 -1 1 -1 1 -1 1 -1 1 1 0 0 0 0 0 0 0 1
AltInvT-1(n, k), 0 ≤ k ≤ nmissing1 -1 1 -1 0 1 -1 1 -1 1 -1 0 0 0 1 -1 1 0 0 -1 1 1 0 -1 0 -1 0 1 -3 3 -1 1 -1 1 -1 1 -1 0 0 0 0 0 0
AltRevInvT-1(n, n - k), 0 ≤ k ≤ nmissing1 1 -1 1 0 -1 1 -1 1 -1 1 0 0 0 -1 1 -1 0 0 1 -1 1 0 -1 0 -1 0 1 1 -1 1 -1 1 -1 3 -3 1 0 0 0 0 0 0
AltInvRev(T(n, n - k))-1, 0 ≤ k ≤ nA0479991 1 1 -1 0 1 -1 -1 1 1 -1 0 0 0 1 -1 -1 0 0 1 1 1 0 -1 0 -1 0 1 1 1 -1 -1 -1 -1 1 1 -1 0 0 0 0 0 0
AltAccsee docsmissing1 1 0 1 1 2 1 0 1 0 1 1 1 1 2 1 0 0 0 1 0 1 1 2 2 3 3 4 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 2 1 0 0 0 0
AltAccRevsee docsmissing1 -1 0 1 1 2 -1 0 -1 0 1 1 1 1 2 -1 0 0 0 -1 0 1 1 2 2 3 3 4 -1 0 -1 0 -1 0 -1 0 1 1 1 1 1 1 1 1 2
AltAntiDiagsee docsmissing1 1 1 -1 1 0 1 -1 1 1 0 1 1 -1 0 -1 1 0 0 0 1 -1 1 0 1 1 0 1 0 1 1 -1 0 -1 1 -1 1 0 0 0 1 0 1 -1 1
AltDiffx1T(n, k) (k+1)missing1 1 -2 1 0 3 1 -2 3 -4 1 0 0 0 5 1 -2 0 0 5 -6 1 0 3 0 5 0 7 1 -2 3 -4 5 -6 7 -8 1 0 0 0 0 0 0 0 9
AltRowSum∑ k=0..n T(n, k)A0013161 0 2 0 2 0 4 0 2 0 4 0 4 0 8 0 2 0 4 0 4 0 8 0 4 0 8 0 8 0 16 0 2 0 4 0 4 0 8 0 4 0 8 0 8 0 16 0
AltEvenSum∑ k=0..n T(n, k) even(k)A0606321 1 2 2 2 2 4 4 2 2 4 4 4 4 8 8 2 2 4 4 4 4 8 8 4 4 8 8 8 8 16 16 2 2 4 4 4 4 8 8 4 4 8 8 8 8 16 16
AltOddSum∑ k=0..n T(n, k) odd(k)A0013160 -1 0 -2 0 -2 0 -4 0 -2 0 -4 0 -4 0 -8 0 -2 0 -4 0 -4 0 -8 0 -4 0 -8 0 -8 0 -16 0 -2 0 -4 0 -4 0
AltAltSum∑ k=0..n T(n, k) (-1)^kA0013161 2 2 4 2 4 4 8 2 4 4 8 4 8 8 16 2 4 4 8 4 8 8 16 4 8 8 16 8 16 16 32 2 4 4 8 4 8 8 16 4 8 8 16 8
AltAbsSum∑ k=0..n | T(n, k) |A0013161 2 2 4 2 4 4 8 2 4 4 8 4 8 8 16 2 4 4 8 4 8 8 16 4 8 8 16 8 16 16 32 2 4 4 8 4 8 8 16 4 8 8 16 8
AltDiagSum∑ k=0..n // 2 T(n - k, k)missing1 1 0 1 1 2 -1 1 2 3 -1 2 1 3 -2 1 3 4 -1 3 2 5 -3 2 3 5 -2 3 1 4 -3 1 4 5 -1 4 3 7 -4 3 5 8 -3 5 2
AltAccSum∑ k=0..n ∑ j=0..k T(n, j)missing1 1 4 2 6 2 16 4 10 2 24 4 28 4 64 8 18 2 40 4 44 4 96 8 52 4 112 8 120 8 256 16 34 2 72 4 76 4 160
AltAccRevSum∑ k=0..n ∑ j=0..k T(n, n - j)missing1 -1 4 -2 6 -2 16 -4 10 -2 24 -4 28 -4 64 -8 18 -2 40 -4 44 -4 96 -8 52 -4 112 -8 120 -8 256 -16 34
AltRowLcmLcm k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
AltRowGcdGcd k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
AltRowMaxMax k=0..n | T(n, k) |A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
AltColMiddleT(n, n // 2)A2092291 1 0 -1 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
AltCentralET(2 n, n)A0000071 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
AltCentralOT(2 n + 1, n)A2092291 -1 0 -1 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0
AltColLeftT(n, 0)A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
AltBinConv∑ k=0..n C(n, k) T(n, k)missing1 0 2 0 2 0 32 0 2 0 92 0 992 0 8192 0 2 0 308 0 9692 0 164320 0 1470944 0 13748672 0 67100672 0
AltInvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^kA0885601 -2 2 -8 2 -12 32 -128 2 -20 92 -464 992 -4032 8192 -32768 2 -36 308 -2320 9692 -52712 164320
AltTransNat0∑ k=0..n T(n, k) kmissing0 -1 2 -2 4 -2 12 -4 8 -2 20 -4 24 -4 56 -8 16 -2 36 -4 40 -4 88 -8 48 -4 104 -8 112 -8 240 -16 32
AltTransNat1∑ k=0..n T(n, k) (k + 1)missing1 -1 4 -2 6 -2 16 -4 10 -2 24 -4 28 -4 64 -8 18 -2 40 -4 44 -4 96 -8 52 -4 112 -8 120 -8 256 -16 34
AltTransSqrs∑ k=0..n T(n, k) k^2missing0 -1 4 -6 16 -10 56 -28 64 -18 168 -44 224 -52 560 -120 256 -34 584 -76 672 -84 1520 -184 896 -100
AltPosHalf∑ k=0..n 2^n T(n, k) (1/2)^kmissing1 1 5 5 17 17 85 85 257 257 1285 1285 4369 4369 21845 21845 65537 65537 327685 327685 1114129
AltNegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^kA0013171 -3 5 -15 17 -51 85 -255 257 -771 1285 -3855 4369 -13107 21845 -65535 65537 -196611 327685 -983055
AltDiagRow1T(n + 1, n)A0000351 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
AltDiagRow3T(n + 3, n)A1212621 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
AltDiagCol1T(n + 1, 1)A000035-1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0
AltDiagCol2T(n + 2, 2)A1338721 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0
AltDiagCol3T(n + 3, 3)A121262-1 0 0 0 -1 0 0 0 -1 0 0 0 -1 0 0 0 -1 0 0 0 -1 0 0 0 -1 0 0 0 -1 0 0 0 -1 0 0 0 -1 0 0 0 -1 0 0 0
AltPolysee docsmissing1 1 1 1 0 1 1 2 -1 1 1 0 5 -2 1 1 2 -5 10 -3 1 1 0 17 -20 17 -4 1 1 4 -17 82 -51 26 -5 1 1 0 85
AltPolyRow1∑ k=0..1 T(1, k) n^kA0000271 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
AltPolyRow2∑ k=0..2 T(2, k) n^kA0025221 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730
AltPolyRow3∑ k=0..3 T(3, k) n^kA0621581 0 -5 -20 -51 -104 -185 -300 -455 -656 -909 -1220 -1595 -2040 -2561 -3164 -3855 -4640 -5525 -6516
AltPolyCol3∑ k=0..n T(n, k) 3^kmissing1 -2 10 -20 82 -164 820 -1640 6562 -13124 65620 -131240 538084 -1076168 5380840 -10761680 43046722
AltPolyDiag∑ k=0..n T(n, k) n^kmissing1 0 5 -20 257 -2504 47989 -720600 16777217 -344373776 10100000101 -261517836040 8916530450689
InvTriangleT(n, k), 0 ≤ k ≤ nA0479991 -1 1 -1 0 1 1 -1 -1 1 -1 0 0 0 1 1 -1 0 0 -1 1 1 0 -1 0 -1 0 1 -1 1 1 -1 1 -1 -1 1 -1 0 0 0 0 0 0
InvRevT(n, n - k), 0 ≤ k ≤ nA0479991 1 -1 1 0 -1 1 -1 -1 1 1 0 0 0 -1 1 -1 0 0 -1 1 1 0 -1 0 -1 0 1 1 -1 -1 1 -1 1 1 -1 1 0 0 0 0 0 0
InvRevInvT-1(n, n - k), 0 ≤ k ≤ nA0479991 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0
InvInvRev(T(n, n - k))-1, 0 ≤ k ≤ nmissing1 -1 1 -1 0 1 -3 1 1 1 -1 0 0 0 1 -3 1 0 0 1 1 -3 0 1 0 1 0 1 5 -1 -1 -1 -1 -1 -1 1 -1 0 0 0 0 0 0
InvAccsee docsA2904521 -1 0 -1 -1 0 1 0 -1 0 -1 -1 -1 -1 0 1 0 0 0 -1 0 1 1 0 0 -1 -1 0 -1 0 1 0 1 0 -1 0 -1 -1 -1 -1 -1
InvAccRevsee docsA2904521 1 0 1 1 0 1 0 -1 0 1 1 1 1 0 1 0 0 0 -1 0 1 1 0 0 -1 -1 0 1 0 -1 0 -1 0 1 0 1 1 1 1 1 1 1 1 0 1 0
InvDiffx1T(n, k) (k+1)missing1 -1 2 -1 0 3 1 -2 -3 4 -1 0 0 0 5 1 -2 0 0 -5 6 1 0 -3 0 -5 0 7 -1 2 3 -4 5 -6 -7 8 -1 0 0 0 0 0 0
InvRowSum∑ k=0..n T(n, k)A0000071 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
InvOddSum∑ k=0..n T(n, k) odd(k)A0635240 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
InvAltSum∑ k=0..n T(n, k) (-1)^kA1307061 -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
InvAbsSum∑ k=0..n | T(n, k) |A0013161 2 2 4 2 4 4 8 2 4 4 8 4 8 8 16 2 4 4 8 4 8 8 16 4 8 8 16 8 16 16 32 2 4 4 8 4 8 8 16 4 8 8 16 8
InvAccSum∑ k=0..n ∑ j=0..k T(n, j)A0482981 -1 -2 0 -4 0 0 0 -8 0 0 0 0 0 0 0 -16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 0 0 0 0 0 0 0 0 0 0 0 0 0
InvAccRevSum∑ k=0..n ∑ j=0..k T(n, n - j)A0482981 1 2 0 4 0 0 0 8 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
InvRowLcmLcm k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
InvRowGcdGcd k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
InvRowMaxMax k=0..n | T(n, k) |A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
InvColMiddleT(n, n // 2)A2092291 -1 0 -1 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
InvCentralET(2 n, n)A0000071 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
InvCentralOT(2 n + 1, n)A209229-1 -1 0 -1 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0
InvColRightT(n, n)A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
InvBinConv∑ k=0..n C(n, k) T(n, k)missing1 0 0 -4 0 -8 -28 0 0 -16 -88 0 -988 0 0 1088 0 -32 -304 0 -9688 0 0 -235840 -1470940 0 0 -4264624
InvInvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 2 0 0 0 0 -28 -96 0 0 -88 -416 -988 -3976 0 0 0 0 -304 -2240 -9688 -52624 0 0 -1470940 -6249048 0
InvTransNat0∑ k=0..n T(n, k) kA0482980 1 2 0 4 0 0 0 8 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
InvTransNat1∑ k=0..n T(n, k) (k + 1)A0482981 1 2 0 4 0 0 0 8 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
InvTransSqrs∑ k=0..n T(n, k) k^2missing0 1 4 4 16 8 16 0 64 16 32 0 64 0 0 0 256 32 64 0 128 0 0 0 256 0 0 0 0 0 0 0 1024 64 128 0 256 0 0
InvNegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^kA1007441 3 -3 -9 -15 -45 45 135 -255 -765 765 2295 3825 11475 -11475 -34425 -65535 -196605 196605 589815
InvDiagRow1T(n + 1, n)A000035-1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0
InvDiagRow2T(n + 2, n)A133872-1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0
InvDiagRow3T(n + 3, n)A1212621 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
InvDiagCol3T(n + 3, 3)A1212621 0 0 0 -1 0 0 0 -1 0 0 0 1 0 0 0 -1 0 0 0 1 0 0 0 1 0 0 0 -1 0 0 0 -1 0 0 0 1 0 0 0 1 0 0 0 -1 0 0
InvPolysee docsmissing1 -1 1 -1 0 1 1 0 1 1 -1 0 3 2 1 1 0 3 8 3 1 1 0 15 16 15 4 1 -1 0 15 80 45 24 5 1 -1 0 45 160 255
InvPolyRow1∑ k=0..1 T(1, k) n^kA000027-1 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
InvPolyRow2∑ k=0..2 T(2, k) n^kA005563-1 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
InvPolyRow3∑ k=0..3 T(3, k) n^kA1526181 0 3 16 45 96 175 288 441 640 891 1200 1573 2016 2535 3136 3825 4608 5491 6480 7581 8800 10143
InvPolyCol2∑ k=0..n T(n, k) 2^kA1007351 1 3 3 15 15 45 45 255 255 765 765 3825 3825 11475 11475 65535 65535 196605 196605 983025 983025
InvPolyCol3∑ k=0..n T(n, k) 3^kA1007361 2 8 16 80 160 640 1280 6560 13120 52480 104960 524800 1049600 4198400 8396800 43046720 86093440
InvPolyDiag∑ k=0..n T(n, k) n^kmissing1 0 3 16 255 2496 45325 691200 16777215 344373760 9899999901 257230656000 8915670445825
Inv:RevTriangleT(n, k), 0 ≤ k ≤ nA0479991 1 -1 1 0 -1 1 -1 -1 1 1 0 0 0 -1 1 -1 0 0 -1 1 1 0 -1 0 -1 0 1 1 -1 -1 1 -1 1 1 -1 1 0 0 0 0 0 0
Inv:RevRevT(n, n - k), 0 ≤ k ≤ nA0479991 -1 1 -1 0 1 1 -1 -1 1 -1 0 0 0 1 1 -1 0 0 -1 1 1 0 -1 0 -1 0 1 -1 1 1 -1 1 -1 -1 1 -1 0 0 0 0 0 0
Inv:RevInvT-1(n, k), 0 ≤ k ≤ nmissing1 -1 1 -1 0 1 -3 1 1 1 -1 0 0 0 1 -3 1 0 0 1 1 -3 0 1 0 1 0 1 5 -1 -1 -1 -1 -1 -1 1 -1 0 0 0 0 0 0
Inv:RevRevInvT-1(n, n - k), 0 ≤ k ≤ nmissing1 1 -1 1 0 -1 1 1 1 -3 1 0 0 0 -1 1 1 0 0 1 -3 1 0 1 0 1 0 -3 1 -1 -1 -1 -1 -1 -1 5 1 0 0 0 0 0 0 0
Inv:RevInvRev(T(n, n - k))-1, 0 ≤ k ≤ nA0479991 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0
Inv:RevAccsee docsA2904521 1 0 1 1 0 1 0 -1 0 1 1 1 1 0 1 0 0 0 -1 0 1 1 0 0 -1 -1 0 1 0 -1 0 -1 0 1 0 1 1 1 1 1 1 1 1 0 1 0
Inv:RevAccRevsee docsA2904521 -1 0 -1 -1 0 1 0 -1 0 -1 -1 -1 -1 0 1 0 0 0 -1 0 1 1 0 0 -1 -1 0 -1 0 1 0 1 0 -1 0 -1 -1 -1 -1 -1
Inv:RevAntiDiagsee docsmissing1 1 1 -1 1 0 1 -1 -1 1 0 -1 1 -1 0 1 1 0 0 0 1 -1 -1 0 -1 1 0 -1 0 -1 1 -1 0 1 -1 1 1 0 0 0 -1 0 1
Inv:RevDiffx1T(n, k) (k+1)missing1 1 -2 1 0 -3 1 -2 -3 4 1 0 0 0 -5 1 -2 0 0 -5 6 1 0 -3 0 -5 0 7 1 -2 -3 4 -5 6 7 -8 1 0 0 0 0 0 0
Inv:RevRowSum∑ k=0..n T(n, k)A0000071 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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:RevEvenSum∑ k=0..n T(n, k) even(k)A0195901 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:RevOddSum∑ k=0..n T(n, k) odd(k)A0635240 -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:RevAltSum∑ k=0..n T(n, k) (-1)^kA1307061 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
Inv:RevAbsSum∑ k=0..n | T(n, k) |A0013161 2 2 4 2 4 4 8 2 4 4 8 4 8 8 16 2 4 4 8 4 8 8 16 4 8 8 16 8 16 16 32 2 4 4 8 4 8 8 16 4 8 8 16 8
Inv:RevDiagSum∑ k=0..n // 2 T(n - k, k)A0055901 1 0 1 -1 0 1 1 -2 -1 1 0 1 1 0 1 -3 -2 1 -1 2 1 -1 0 1 1 0 1 -1 0 1 1 -4 -3 1 -2 3 1 -2 -1 3 2 -1
Inv:RevAccSum∑ k=0..n ∑ j=0..k T(n, j)A0482981 1 2 0 4 0 0 0 8 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Inv:RevAccRevSum∑ k=0..n ∑ j=0..k T(n, n - j)A0482981 -1 -2 0 -4 0 0 0 -8 0 0 0 0 0 0 0 -16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 0 0 0 0 0 0 0 0 0 0 0 0 0
Inv:RevRowLcmLcm k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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:RevRowGcdGcd k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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:RevRowMaxMax k=0..n | T(n, k) |A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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:RevColMiddleT(n, n // 2)A2092291 1 0 -1 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Inv:RevCentralET(2 n, n)A0000071 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Inv:RevCentralOT(2 n + 1, n)A2092291 -1 0 1 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
Inv:RevColLeftT(n, 0)A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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:RevBinConv∑ k=0..n C(n, k) T(n, k)missing1 0 0 -4 0 -8 -28 0 0 -16 -88 0 -988 0 0 1088 0 -32 -304 0 -9688 0 0 -235840 -1470940 0 0 -4264624
Inv:RevInvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -2 0 0 0 0 -28 96 0 0 -88 416 -988 3976 0 0 0 0 -304 2240 -9688 52624 0 0 -1470940 6249048 0 0 0
Inv:RevTransNat0∑ k=0..n T(n, k) kA0482980 -1 -2 0 -4 0 0 0 -8 0 0 0 0 0 0 0 -16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 0 0 0 0 0 0 0 0 0 0 0 0 0
Inv:RevTransNat1∑ k=0..n T(n, k) (k + 1)A0482981 -1 -2 0 -4 0 0 0 -8 0 0 0 0 0 0 0 -16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 0 0 0 0 0 0 0 0 0 0 0 0 0
Inv:RevTransSqrs∑ k=0..n T(n, k) k^2missing0 -1 -4 4 -16 8 16 0 -64 16 32 0 64 0 0 0 -256 32 64 0 128 0 0 0 256 0 0 0 0 0 0 0 -1024 64 128 0
Inv:RevPosHalf∑ k=0..n 2^n T(n, k) (1/2)^kA1007351 1 3 3 15 15 45 45 255 255 765 765 3825 3825 11475 11475 65535 65535 196605 196605 983025 983025
Inv:RevNegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^kA1007441 -3 3 -9 15 -45 45 -135 255 -765 765 -2295 3825 -11475 11475 -34425 65535 -196605 196605 -589815
Inv:RevDiagRow3T(n + 3, n)A1212621 0 0 0 -1 0 0 0 -1 0 0 0 1 0 0 0 -1 0 0 0 1 0 0 0 1 0 0 0 -1 0 0 0 -1 0 0 0 1 0 0 0 1 0 0 0 -1 0 0
Inv:RevDiagCol1T(n + 1, 1)A000035-1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0
Inv:RevDiagCol2T(n + 2, 2)A133872-1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0
Inv:RevDiagCol3T(n + 3, 3)A1212621 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
Inv:RevPolysee docsmissing1 1 1 1 0 1 1 0 -1 1 1 0 -3 -2 1 1 0 3 -8 -3 1 1 0 -15 16 -15 -4 1 1 0 15 -80 45 -24 -5 1 1 0 45
Inv:RevPolyRow1∑ k=0..1 T(1, k) n^kA0000271 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:RevPolyRow2∑ k=0..2 T(2, k) n^kA0055631 0 -3 -8 -15 -24 -35 -48 -63 -80 -99 -120 -143 -168 -195 -224 -255 -288 -323 -360 -399 -440 -483
Inv:RevPolyRow3∑ k=0..3 T(3, k) n^kA1526181 0 3 16 45 96 175 288 441 640 891 1200 1573 2016 2535 3136 3825 4608 5491 6480 7581 8800 10143
Inv:RevPolyCol3∑ k=0..n T(n, k) 3^kA1007361 -2 -8 16 -80 160 640 -1280 -6560 13120 52480 -104960 524800 -1049600 -4198400 8396800 -43046720
Inv:RevPolyDiag∑ k=0..n T(n, k) n^kmissing1 0 -3 16 -255 2496 45325 -691200 -16777215 344373760 9899999901 -257230656000 8915670445825
 << TableSourceSimilarsIndex >> 

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.