A148745 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, 1), (-1, 1, 0), (1, 0, -1), (1, 0, 1)}.

1, 1, 3, 7, 27, 81, 311, 1021, 4297, 15419, 64017, 234823, 1027493, 3966913, 17125911, 66455693, 297225631, 1194038589, 5276016417, 21192497825, 96118467609, 396039404493, 1776784716427, 7306320511915, 33459539888437, 140337672765695, 636370828530161, 2661670399860595, 12275747222956889

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 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, -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: A148742 A148743 A148744 * A148746 A148747 A216078

Adjacent sequences: A148742 A148743 A148744 * A148746 A148747 A148748

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved