A148049 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, 1, 1), (1, -1, -1)}.

1, 1, 2, 3, 10, 20, 58, 139, 438, 1140, 3418, 9932, 30628, 88108, 280662, 840825, 2681258, 8069994, 26491824, 81571012, 264345958, 834289608, 2744822564, 8655497466, 28654030002, 91833730268, 305378072266, 978386996766, 3289069655984, 10666263089892, 35684640821198, 116837930295941, 393934299599316

Offset

0,3

Links

Table of n, a(n) for n=0..32.

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[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: A148046 A148047 A148048 * A148050 A148051 A148052

Adjacent sequences: A148046 A148047 A148048 * A148050 A148051 A148052

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved