A149158 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, 1), (-1, 1, 0), (-1, 1, 1), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 9, 39, 112, 514, 1664, 7851, 27382, 131105, 481129, 2325552, 8853388, 43081144, 168640035, 824599205, 3299204419, 16190983750, 65931058149, 324475345942, 1340598991785, 6612464402576, 27654162310720, 136650279385596, 577427106053159, 2857535277900956, 12182684785904000, 60363307435355304

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A149155 A149156 A149157 * A142239 A118639 A149159

Adjacent sequences: A149155 A149156 A149157 * A149159 A149160 A149161

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved