A151016 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), (1, -1, 1), (1, 1, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 39, 185, 876, 4272, 20822, 102663, 506407, 2511487, 12460241, 61987781, 308486218, 1537481126, 7664734089, 38242778515, 190848327321, 952890984361, 4758408361998, 23769042156759, 118743134456250, 593318364722098, 2964839633443516, 14817246566131697, 74055736485350895, 370155808721123557

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + 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: A151013 A151014 A151015 * A151017 A151018 A096359

Adjacent sequences: A151013 A151014 A151015 * A151017 A151018 A151019

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved