A149509 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), (0, 0, -1), (1, -1, -1), (1, 1, 1)}.

1, 1, 5, 11, 47, 155, 579, 2233, 8593, 33469, 135037, 537525, 2178673, 8924945, 36519777, 150647219, 626290259, 2602163219, 10874068199, 45661251703, 191802674707, 808778179043, 3422465929651, 14489849379543, 61521249901323, 261890744544831, 1115495062342795, 4761600058102759

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[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, j, 1 + 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: A149506 A149507 A149508 * A149510 A149511 A149512

Adjacent sequences: A149506 A149507 A149508 * A149510 A149511 A149512

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved