A148243 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, 1), (1, 0, 0)}.

1, 1, 2, 4, 13, 36, 115, 358, 1162, 3846, 13131, 45774, 160487, 570699, 2038537, 7365489, 26832702, 98727890, 365178878, 1358061230, 5072922935, 19034627200, 71768522621, 271873506868, 1034051230202, 3945442312974, 15099285947998, 57945734250270, 223015892379970, 860798756426298, 3331476814130518

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, -1 + 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: A151354 A148241 A148242 * A148244 A148245 A148246

Adjacent sequences: A148240 A148241 A148242 * A148244 A148245 A148246

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved