A149701 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, 1)}.

1, 1, 5, 17, 69, 277, 1177, 4997, 21743, 95197, 421221, 1876235, 8408775, 37879153, 171377779, 778373055, 3546990371, 16211876805, 74293350841, 341275455053, 1571058166151, 7246536397095, 33484494259497, 154977708854283, 718373025302315, 3334547958542677, 15498365157356255, 72120349103863425

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[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: A151276 A272743 A149700 * A149702 A273331 A149703

Adjacent sequences: A149698 A149699 A149700 * A149702 A149703 A149704

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved