A148196 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), (0, 1, 0), (1, -1, 0), (1, 1, -1)}.

1, 1, 2, 4, 12, 33, 103, 341, 1180, 4238, 15559, 59000, 228138, 899193, 3600197, 14613307, 60110586, 249975610, 1050141697, 4450881876, 19018293897, 81879346052, 354908343163, 1547962863230, 6789898297183, 29940096151663, 132670584126911, 590559290581918, 2639841539823471, 11846460906971781

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 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: A169807 A005028 A231356 * A148197 A148198 A148199

Adjacent sequences: A148193 A148194 A148195 * A148197 A148198 A148199

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved