A148976 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, 0), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 9, 32, 107, 411, 1553, 6194, 24389, 100612, 412488, 1734453, 7264212, 31092761, 132827500, 575349257, 2489633556, 10903009511, 47736774170, 210767379271, 930722838057, 4140160460869, 18425314173567, 82449058082568, 369170820588110, 1660949457878375, 7478371588472407, 33798023245901890

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[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148973 A148974 A148975 * A148977 A202143 A330464

Adjacent sequences: A148973 A148974 A148975 * A148977 A148978 A148979

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved