A151199 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, 1, -1), (0, 1, 1), (1, 0, 0), (1, 1, 1)}

1, 3, 12, 53, 242, 1131, 5375, 25770, 124613, 606018, 2959699, 14507794, 71303815, 351256141, 1733644863, 8569727681, 42418344280, 210196707443, 1042591974695, 5175657001614, 25711584348853, 127810271426162, 635686118474741, 3163229223668441, 15747294822922287, 78423745649255033

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + 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: A228771 A370023 A151198 * A151200 A151201 A151202

Adjacent sequences: A151196 A151197 A151198 * A151200 A151201 A151202

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved