A148990 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, 1), (0, 1, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 3, 9, 33, 115, 441, 1643, 6407, 24603, 96779, 377445, 1492297, 5871099, 23287029, 92099083, 366082077, 1452638305, 5782634569, 22995888507, 91639232473, 364963107847, 1455530408507, 5802819699999, 23156241508257, 92386637441455, 368837264732893, 1472357214006587, 5880195295415315

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148988 A148989 A047117 * A184512 A148991 A148992

Adjacent sequences: A148987 A148988 A148989 * A148991 A148992 A148993

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved