A149087 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), (0, 0, -1), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 7, 30, 75, 293, 897, 3296, 11493, 41905, 153503, 570138, 2136265, 8128562, 30938365, 119262756, 461558439, 1797401295, 7047184967, 27701702878, 109512364145, 434806576518, 1730879700961, 6923437993554, 27750890786575, 111617155390501, 450364141890515, 1820424319409176

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[-1 + i, j, 1 + k, -1 + n] + aux[i, j, 1 + 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: A149084 A149085 A149086 * A149088 A047004 A030689

Adjacent sequences: A149084 A149085 A149086 * A149088 A149089 A149090

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved