A149737 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), (0, 0, -1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 77, 297, 1373, 5809, 27253, 120329, 570573, 2586625, 12364485, 57069913, 274465917, 1283251825, 6200548277, 29271883273, 141965261869, 675241861857, 3284705374821, 15716823889401, 76644108947421, 368511402314065, 1800809591628437, 8693144347330793, 42556047614537869, 206122190131352257

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, 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: A149736 A145959 A126956 * A149738 A149739 A149740

Adjacent sequences: A149734 A149735 A149736 * A149738 A149739 A149740

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved