A150711 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), (0, 0, 1), (0, 1, -1), (1, 0, 1), (1, 1, -1)}.

1, 2, 8, 27, 122, 491, 2307, 10018, 48090, 217772, 1058048, 4917256, 24072412, 113814946, 560021422, 2679737850, 13232592446, 63871995263, 316217434327, 1536297783020, 7620579664963, 37208343869514, 184838042046015, 906010500949829, 4505884504381738, 22154601764818605, 110281283086960892

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A305256 A323613 A150710 * A150712 A150713 A276940

Adjacent sequences: A150708 A150709 A150710 * A150712 A150713 A150714

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved