A149226 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, 1), (-1, 0, 1), (-1, 1, 1), (1, 0, -1), (1, 1, 0)}

1, 1, 4, 10, 45, 137, 651, 2225, 10782, 39551, 193668, 744173, 3667892, 14564363, 72089043, 293344604, 1456043669, 6038218547, 30028994375, 126420217768, 629561111620, 2683075985049, 13374552608998, 57581209527148, 287235901179914, 1247233541894547, 6224972949360422, 27227496594651898

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, k, -1 + n] + aux[-1 + i, 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, -1 + 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: A052394 A197627 A066229 * A155386 A155330 A155278

Adjacent sequences: A149223 A149224 A149225 * A149227 A149228 A149229

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved