A150404 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, 1, 0), (0, 0, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 7, 24, 93, 370, 1532, 6489, 28073, 123084, 547636, 2456285, 11132291, 50748503, 233047306, 1075234895, 4987712376, 23224769741, 108598776603, 509369414469, 2397252200499, 11310787222758, 53515495787157, 253742557854070, 1205895541391462, 5741448946494024, 27389182382157154, 130865542615266679

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150402 A151295 A150403 * A150405 A150406 A150407

Adjacent sequences: A150401 A150402 A150403 * A150405 A150406 A150407

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved