A148529 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, 1, -1), (-1, 1, 0), (1, 0, 0)}.

1, 1, 3, 5, 19, 39, 160, 363, 1563, 3779, 16780, 42371, 192044, 500434, 2303127, 6147873, 28618129, 77852757, 365637202, 1010042925, 4777539602, 13365767718, 63586163133, 179792193630, 859444875265, 2452244379804, 11769396623750, 33845097492968, 162992466264148, 471920275052591, 2279362650011522

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[1 + i, -1 + j, k, -1 + n] + aux[1 + 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: A148526 A148527 A148528 * A148530 A148531 A148532

Adjacent sequences: A148526 A148527 A148528 * A148530 A148531 A148532

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved