A149011 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), (0, 1, -1), (0, 1, 1), (1, -1, 1)}.

1, 1, 3, 9, 34, 125, 498, 1995, 8275, 34635, 147828, 635203, 2764589, 12100073, 53407392, 236872232, 1056879553, 4734289388, 21303849938, 96179139060, 435755416559, 1979716310445, 9019780037245, 41191397377348, 188552701333284, 864826450474272, 3974462412630393, 18296975043799806

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[i, -1 + j, -1 + k, -1 + n] + aux[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: A149008 A149009 A149010 * A149012 A145090 A273095

Adjacent sequences: A149008 A149009 A149010 * A149012 A149013 A149014

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved