A148761 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), (-1, 1, -1), (0, 1, 1), (1, -1, 0), (1, -1, 1)}.

1, 1, 3, 7, 29, 78, 338, 1058, 4698, 15815, 71857, 254131, 1171908, 4300017, 20035297, 75618646, 355106839, 1370474585, 6475644291, 25446998630, 120843594317, 482024049999, 2298547334634, 9284776929847, 44428692153983, 181411707530385, 870640865259852, 3588376805328084, 17265370230610681

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, 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, -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: A363666 A148759 A148760 * A186732 A148762 A096064

Adjacent sequences: A148758 A148759 A148760 * A148762 A148763 A148764

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved