A148466 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, 1), (0, 0, 1), (1, 1, -1)}.

1, 1, 2, 6, 19, 61, 221, 815, 3095, 12109, 48260, 195368, 803053, 3337237, 14015560, 59384502, 253544419, 1090093997, 4715233418, 20507407116, 89633056681, 393499148239, 1734526536805, 7673967478285, 34066109008637, 151697174130059, 677446012298428, 3033350909365552, 13615684209776521

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, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + 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: A289591 A148464 A148465 * A094817 A033565 A094831

Adjacent sequences: A148463 A148464 A148465 * A148467 A148468 A148469

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved