A150603 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, 0, 1), (0, 1, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 7, 27, 110, 472, 2077, 9345, 42672, 197231, 920109, 4325028, 20456323, 97251702, 464357938, 2225412247, 10699151819, 51580477446, 249269706390, 1207192943591, 5857368451966, 28468107671277, 138570095211652, 675414937449190, 3296144191756004, 16103773890351584, 78757640197138906

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, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A005768 A150601 A150602 * A150604 A150605 A150606

Adjacent sequences: A150600 A150601 A150602 * A150604 A150605 A150606

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved