A149990 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), (-1, 1, 0), (0, 1, 1), (1, 0, 0)}.

1, 2, 5, 17, 57, 207, 765, 2909, 11291, 44081, 175584, 703093, 2841402, 11564076, 47337597, 194895967, 805502604, 3345308673, 13940425210, 58284862481, 244441854605, 1027943841626, 4333816696752, 18311937717644, 77543896603410, 329004496264711, 1398418407733861, 5954013641050949

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A149988 A148412 A149989 * A149991 A149992 A134128

Adjacent sequences: A149987 A149988 A149989 * A149991 A149992 A149993

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved