A149750 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, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 81, 319, 1565, 6763, 33223, 149513, 739755, 3425529, 16972105, 79927467, 397118453, 1894350891, 9420434485, 45329871053, 225728778329, 1093736644385, 5449569533029, 26539366097687, 132332738691287, 647153828039847, 3228097425186269, 15837292116979379, 79034503921927555

Offset

0,3

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, 1 + k, -1 + n] + aux[-1 + i, 1 + 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: A151882 A359206 A149749 * A179605 A149751 A303713

Adjacent sequences: A149747 A149748 A149749 * A149751 A149752 A149753

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved