A150601 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, 0, 0), (0, -1, 1), (0, 0, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 7, 27, 110, 468, 2054, 9190, 41772, 192237, 893133, 4182486, 19714258, 93429325, 444835299, 2126344430, 10198950881, 49065491000, 236665988835, 1144204335949, 5543289980742, 26904984196401, 130803077926028, 636873031138093, 3105106813756143, 15157789417360378, 74077123589403300

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, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150599 A150600 A005768 * A150602 A150603 A150604

Adjacent sequences: A150598 A150599 A150600 * A150602 A150603 A150604

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved