A148182 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, 0, 1), (1, 0, -1)}.

1, 1, 2, 4, 12, 29, 93, 266, 889, 2819, 9704, 32547, 114559, 402548, 1447243, 5232685, 19135813, 70627631, 263062730, 986459954, 3723667384, 14131582708, 54009336165, 207318335930, 800149593714, 3098358305471, 12056855792087, 47090041195574, 184619039183558, 726005646404804, 2863646013210247

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, 1 + k, -1 + n] + aux[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, 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: A148180 A148181 A331687 * A148183 A148184 A148185

Adjacent sequences: A148179 A148180 A148181 * A148183 A148184 A148185

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved