A150406 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), (1, 0, 0), (1, 1, -1), (1, 1, 0)}.

1, 2, 7, 24, 93, 375, 1568, 6738, 29524, 131397, 592474, 2699383, 12408001, 57468088, 267866657, 1255563128, 5913784441, 27972890308, 132815595779, 632722358676, 3023272574031, 14484726323390, 69565951887442, 334840925316058, 1614913283611508, 7802839738638430, 37764381640320588, 183053879521094349

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, 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: A150403 A150404 A150405 * A150407 A317130 A150408

Adjacent sequences: A150403 A150404 A150405 * A150407 A150408 A150409

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved