A148842 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, 0, 0), (0, -1, 1), (0, 1, 0), (1, -1, 1), (1, 0, -1)}.

1, 1, 3, 8, 27, 93, 341, 1295, 5052, 20209, 82190, 339801, 1422276, 6020724, 25727971, 110854465, 481147223, 2101771068, 9234216691, 40779355432, 180925623756, 806086402420, 3605151047127, 16180065798799, 72849331715413, 328964096764340, 1489531226709228, 6761473239089773, 30764122078267794

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A000238 A259811 A148841 * A330783 A148843 A340334

Adjacent sequences: A148839 A148840 A148841 * A148843 A148844 A148845

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved