A148723 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, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 7, 25, 70, 255, 781, 2945, 9566, 36273, 121772, 468394, 1617306, 6235943, 21900361, 85097623, 303805020, 1182002913, 4263539140, 16667966492, 60771203088, 237764335169, 872895295404, 3426343475418, 12674553037840, 49776249130500, 185043376859226, 728431017894926, 2723200393656846

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, j, -1 + k, -1 + n] + aux[1 + 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: A337016 A148721 A148722 * A148724 A332508 A309911

Adjacent sequences: A148720 A148721 A148722 * A148724 A148725 A148726

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved