A151122 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), (0, 0, -1), (0, 1, 0), (1, 0, 1), (1, 1, 0)}.

1, 3, 11, 45, 194, 856, 3874, 17747, 82404, 385417, 1817913, 8615532, 41064328, 196385786, 943020495, 4539619335, 21919591900, 106043626149, 514218649348, 2497339513947, 12150816675285, 59193652656970, 288794116773499, 1410426011238932, 6896686774980053, 33752680421916301, 165354585804989357

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[i, -1 + j, k, -1 + n] + aux[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: A151120 A151121 A142876 * A151123 A151124 A151125

Adjacent sequences: A151119 A151120 A151121 * A151123 A151124 A151125

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved