A148039 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, 1, 0), (0, 0, -1), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 3, 8, 19, 55, 145, 438, 1319, 4258, 13442, 44510, 148574, 512622, 1765355, 6199765, 21989638, 79344998, 287621419, 1052530049, 3883860734, 14482939260, 54310810535, 204858164609, 777520351881, 2972596559904, 11423778936131, 44092393135378, 170962910891491, 666445496840772, 2609633213350411

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A078343 A148038 A326301 * A148040 A148041 A148042

Adjacent sequences: A148036 A148037 A148038 * A148040 A148041 A148042

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved