A149733 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, 0), (0, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 75, 303, 1337, 5943, 26723, 122153, 563311, 2617471, 12248479, 57586121, 272366507, 1292397415, 6155702591, 29418323033, 140956169741, 677110012143, 3259741590865, 15725222821637, 75996265503789, 367860874886273, 1783400454302755, 8657720979324607, 42082514061246075, 204790232187422719

Offset

0,3

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A149730 A149731 A149732 * A149734 A149735 A149736

Adjacent sequences: A149730 A149731 A149732 * A149734 A149735 A149736

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved