A150724 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, 0), (-1, 1, 0), (0, 0, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 28, 120, 498, 2197, 9739, 44038, 200907, 926734, 4298555, 20106220, 94381766, 445676955, 2110996515, 10038809369, 47870526906, 228936102807, 1097319387744, 5271954610386, 25373558850530, 122359721914669, 590924284061347, 2858400266257766, 13843964364288370, 67139289117393321

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[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A150721 A150722 A150723 * A150725 A150726 A150727

Adjacent sequences: A150721 A150722 A150723 * A150725 A150726 A150727

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved