A150138 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, -1), (0, 0, 1), (1, -1, 0), (1, 1, 0)}.

1, 2, 6, 20, 73, 271, 1080, 4279, 17742, 73334, 311463, 1320901, 5714076, 24652208, 108136214, 472772076, 2095411822, 9259635607, 41376583416, 184401748204, 829589409023, 3722631449396, 16842693737703, 76013872054272, 345562604149092, 1567259945508055, 7153952350547666, 32583203020133357

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, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150136 A195186 A150137 * A148481 A150139 A052884

Adjacent sequences: A150135 A150136 A150137 * A150139 A150140 A150141

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved