A149989 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), (-1, 0, 1), (0, 1, 1), (1, 0, 0)}.

1, 2, 5, 17, 57, 207, 765, 2881, 11179, 43677, 173480, 693553, 2797983, 11382137, 46538292, 191449223, 790709157, 3281073206, 13667322149, 57117349582, 239451649152, 1006502550212, 4242216990195, 17921591400135, 75873336597512, 321854231610450, 1367802823437628, 5823075621825059

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, 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: A149987 A149988 A148412 * A149990 A149991 A149992

Adjacent sequences: A149986 A149987 A149988 * A149990 A149991 A149992

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved