A150096 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, 1, -1), (0, 1, 0), (0, 1, 1), (1, 0, -1)}.

1, 2, 6, 19, 67, 245, 943, 3733, 15148, 62691, 263890, 1125435, 4858228, 21183643, 93173701, 413028526, 1843540504, 8278392131, 37380361777, 169626259309, 773179620400, 3538786648904, 16257620999050, 74945848144070, 346593310562478, 1607561199422829, 7476414123371464, 34859423858670421

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + 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: A121655 A250918 A150095 * A150097 A145847 A150098

Adjacent sequences: A150093 A150094 A150095 * A150097 A150098 A150099

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved