A150727 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), (1, 0, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 28, 124, 506, 2325, 10121, 47466, 214129, 1017164, 4692031, 22482423, 105282324, 507640379, 2402998152, 11641232260, 55550981755, 270101725432, 1296919941414, 6324377801704, 30516294036669, 149166338438914, 722606464011632, 3539150056696503, 17200434795171516, 84383788322559388

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[-1 + 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: A150724 A150725 A150726 * A150728 A150729 A075662

Adjacent sequences: A150724 A150725 A150726 * A150728 A150729 A150730

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved