A148809 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, 1), (1, -1, -1), (1, 0, -1)}.

1, 1, 3, 8, 26, 86, 300, 1099, 4065, 15464, 60126, 235711, 938916, 3786566, 15373560, 63058702, 260700178, 1083632350, 4536791630, 19096536008, 80737061523, 343192967447, 1464457668985, 6271953873038, 26975682913289, 116353776657458, 503418109852904, 2185615416588541, 9509539891579458

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, -1 + 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: A148806 A148807 A148808 * A151457 A148810 A148811

Adjacent sequences: A148806 A148807 A148808 * A148810 A148811 A148812

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved