A148246 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, 0), (0, 1, 0), (1, -1, -1), (1, -1, 1)}.

1, 1, 2, 4, 13, 36, 120, 389, 1305, 4343, 15400, 55281, 200856, 739968, 2760315, 10296944, 38804152, 148302743, 570811519, 2207354724, 8597327712, 33619658081, 131780667660, 519451646838, 2060104877690, 8199408491872, 32743528337811, 131224009830536, 527074955118907, 2121770470885508

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[1 + i, j, 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: A148243 A148244 A148245 * A148247 A148248 A148249

Adjacent sequences: A148243 A148244 A148245 * A148247 A148248 A148249

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved