A150944 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, 1, 1), (1, 0, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 34, 159, 686, 3301, 14993, 73230, 342078, 1683261, 8002664, 39548594, 190227852, 942786059, 4571684692, 22702890172, 110740507104, 550721090484, 2698252033461, 13432812136852, 66038808670501, 329028005893039, 1621915437645480, 8085976289028859, 39944465415561639, 199238808563027686

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, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A150941 A150942 A150943 * A276901 A151308 A215943

Adjacent sequences: A150941 A150942 A150943 * A150945 A150946 A150947

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved