A149985 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 0, -1), (0, 0, 1), (1, -1, -1), (1, 1, 0)}.

1, 2, 5, 17, 55, 200, 737, 2810, 10993, 43563, 176307, 717457, 2968511, 12319177, 51739914, 218083622, 926385446, 3953155545, 16951252816, 73047645626, 315747238313, 1371343273755, 5968518947214, 26086649250226, 114220422192153, 501836040308036, 2208889047373640, 9748272309261590

Offset

0,2

Links

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149982 A149983 A149984 * A149986 A121193 A159866

Adjacent sequences: A149982 A149983 A149984 * A149986 A149987 A149988

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved