A148820 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, 0), (0, 0, -1), (1, -1, 1), (1, 0, 1)}.

1, 1, 3, 8, 26, 92, 327, 1177, 4546, 17541, 68673, 277081, 1120356, 4568417, 18983023, 79045293, 331103647, 1404169545, 5966973556, 25469309886, 109652366558, 472967585532, 2047134387062, 8916507100573, 38902775529888, 170205654258331, 748234881202931, 3294329998721192, 14537565236641632

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, 1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A028270 A124383 A148819 * A148821 A074506 A215087

Adjacent sequences: A148817 A148818 A148819 * A148821 A148822 A148823

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved