A149276 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), (0, -1, 1), (0, 1, -1), (1, 1, 0)}.

1, 1, 4, 11, 42, 154, 607, 2457, 10096, 42635, 181063, 783097, 3404412, 14968062, 66152869, 294491008, 1317205403, 5921288039, 26725832213, 121082990990, 550409795013, 2509499048267, 11473203958203, 52583234951938, 241548502218746, 1111869845478979, 5127900552363954, 23691050694984716

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[i, -1 + j, 1 + k, -1 + n] + aux[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: A151427 A149275 A378830 * A149277 A149278 A176645

Adjacent sequences: A149273 A149274 A149275 * A149277 A149278 A149279

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved