A149154 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, 0, 1), (-1, 1, 1), (1, -1, -1), (1, 1, 0)}.

1, 1, 4, 9, 39, 112, 511, 1655, 7754, 27061, 128714, 472720, 2270366, 8651976, 41837362, 163948096, 796796614, 3191331555, 15570137360, 63466080257, 310584371757, 1284389855918, 6300697460577, 26372512380003, 129628574987488, 548174480986494, 2698834335089730, 11513980004561963, 56764309192152032

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, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149152 A149153 A101529 * A149155 A149156 A149157

Adjacent sequences: A149151 A149152 A149153 * A149155 A149156 A149157

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved