A148546 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, -1), (0, 0, -1), (1, 0, 1)}.

1, 1, 3, 5, 19, 51, 173, 531, 1787, 6255, 22357, 78863, 285273, 1035873, 3894181, 14628591, 55113149, 208744661, 798606157, 3087248599, 12007484653, 46699329757, 182421963277, 716322832651, 2829957884247, 11226717483801, 44610013592917, 177643982882589, 709898799672099, 2847093954711881

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[i, 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A065964 A340737 A209778 * A148547 A360086 A127998

Adjacent sequences: A148543 A148544 A148545 * A148547 A148548 A148549

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved