A150118 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, 0), (1, -1, -1), (1, 1, 0)}.

1, 2, 6, 19, 71, 275, 1114, 4651, 19925, 86643, 382655, 1712982, 7743651, 35289178, 162101956, 749571206, 3484376167, 16277276570, 76387977097, 359852913731, 1700945034026, 8065817666940, 38357500715924, 182868252256455, 873854209821109, 4184888850204701, 20080433565203323, 96523687360941940

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[i, -1 + j, 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: A150117 A038392 A044045 * A343417 A150119 A361489

Adjacent sequences: A150115 A150116 A150117 * A150119 A150120 A150121

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved