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 A238344 Irregular triangle T(n,k) read by rows: T(n,k) is the number of compositions of n with k descents, n>=0, 0<=k<=floor(n/3). 14
 1, 1, 2, 3, 1, 5, 3, 7, 9, 11, 19, 2, 15, 41, 8, 22, 77, 29, 30, 142, 81, 3, 42, 247, 205, 18, 56, 421, 469, 78, 77, 689, 1013, 264, 5, 101, 1113, 2059, 786, 37, 135, 1750, 4021, 2097, 189, 176, 2712, 7558, 5179, 751, 8, 231, 4128, 13780, 11998, 2558, 73, 297, 6208, 24440, 26400, 7762, 429 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Same as A238343, with zeros omitted. Columns k=0-10 give: A000041, A241626, A241627, A241628, A241629, A241630, A241631, A241632, A241633, A241634, A241635. Row sums are A011782. T(3n,n) = A000045(n+1). T(3n+1,n) = A136376(n+1). LINKS Joerg Arndt and Alois P. Heinz, Rows n = 0..250, flattened EXAMPLE Triangle starts: 00: 1; 01: 1; 02: 2; 03: 3, 1; 04: 5, 3; 05: 7, 9; 06: 11, 19, 2; 07: 15, 41, 8; 08: 22, 77, 29; 09: 30, 142, 81, 3; 10: 42, 247, 205, 18; 11: 56, 421, 469, 78; 12: 77, 689, 1013, 264, 5; 13: 101, 1113, 2059, 786, 37; 14: 135, 1750, 4021, 2097, 189; 15: 176, 2712, 7558, 5179, 751, 8; 16: 231, 4128, 13780, 11998, 2558, 73; 17: 297, 6208, 24440, 26400, 7762, 429; 18: 385, 9201, 42358, 55593, 21577, 1945, 13; 19: 490, 13502, 71867, 112814, 55867, 7465, 139; 20: 627, 19585, 119715, 221639, 136478, 25317, 927; ... MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, expand( add(b(n-j, j)*`if`(j (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n, 0)): seq(T(n), n=0..20); MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0, 1, Expand[Sum[b[n-j, j]*If[j

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Last modified October 3 17:26 EDT 2023. Contains 365870 sequences. (Running on oeis4.)