A148186 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, 0, 1), (0, 0, -1), (0, 1, 0), (1, -1, 0)}.

1, 1, 2, 4, 12, 30, 89, 264, 884, 2747, 9329, 31445, 112592, 386695, 1404984, 5055108, 18900644, 68752713, 260143007, 974793598, 3755514208, 14179006578, 55137620398, 212489097664, 836744112593, 3242710398416, 12862836044126, 50605909221367, 202622230548568, 800607178797359, 3224291827647012

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A079472 A366590 A308556 * A006948 A148187 A148188

Adjacent sequences: A148183 A148184 A148185 * A148187 A148188 A148189

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved