A150565 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, 1), (0, -1, 1), (0, 1, -1), (0, 1, 0), (1, 1, 0)}.

1, 2, 7, 26, 107, 455, 1997, 8960, 40802, 188190, 876126, 4110613, 19409604, 92128043, 439257473, 2102256709, 10094370187, 48608230113, 234652253431, 1135270546210, 5503323842213, 26724710156090, 129982634911257, 633105351011227, 3087646339418001, 15076130618030798, 73691824779803129

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[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150562 A150563 A150564 * A150566 A150567 A000151

Adjacent sequences: A150562 A150563 A150564 * A150566 A150567 A150568

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved