A148168 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, 1, 1), (0, 0, 1), (0, 1, -1), (1, -1, 1)}.

1, 1, 2, 4, 11, 31, 102, 340, 1203, 4344, 16173, 61520, 238575, 940236, 3756059, 15180801, 62001672, 255519383, 1061764788, 4443897040, 18722145717, 79344717504, 338078438238, 1447629138256, 6226612449561, 26893592839179, 116602739854967, 507350856424816, 2214826529968892, 9698461780045479

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148165 A148166 A148167 * A004251 A148169 A110140

Adjacent sequences: A148165 A148166 A148167 * A148169 A148170 A148171

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved