A149922 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), (-1, 1, -1), (0, 1, 0), (1, 0, 0)}.

1, 2, 5, 15, 47, 158, 551, 1978, 7280, 27287, 103890, 400726, 1562935, 6152911, 24424119, 97651753, 392890089, 1589751091, 6465135718, 26411296607, 108341410515, 446089923524, 1843009043745, 7638272615102, 31747762868828, 132306896027373, 552742459514066, 2314493115874922, 9712068714424451

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A149919 A149920 A149921 * A192053 A013560 A149923

Adjacent sequences: A149919 A149920 A149921 * A149923 A149924 A149925

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved