A148984 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, 0, 0), (-1, 1, 1), (0, -1, 1), (0, 1, 1), (1, 0, -1)}.

1, 1, 3, 9, 32, 112, 431, 1678, 6763, 27670, 115426, 487077, 2082049, 8977804, 39046114, 171030912, 753916676, 3341768584, 14885951812, 66601109529, 299166820070, 1348655444107, 6099540897124, 27668136578751, 125845441835454, 573819151893002, 2622450568940290, 12010412791891348, 55113705601828460

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148981 A148982 A148983 * A289611 A194353 A148985

Adjacent sequences: A148981 A148982 A148983 * A148985 A148986 A148987

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved