A150327 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, 1, 0), (0, 0, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 22, 87, 323, 1342, 5468, 23419, 100418, 440643, 1947254, 8713746, 39265051, 178424429, 815376294, 3749149497, 17318997226, 80376437925, 374471291983, 1750996971807, 8214029567976, 38646789638674, 182322472323533, 862271866845863, 4087275031494930, 19415011169055886, 92402575597208605

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, -1 + j, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A150325 A102311 A150326 * A150328 A150329 A323681

Adjacent sequences: A150324 A150325 A150326 * A150328 A150329 A150330

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved