A150559 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, 0, 0), (0, -1, 0), (0, 1, -1), (0, 1, 0), (1, 0, 1)}.

1, 2, 7, 26, 106, 441, 1913, 8405, 37758, 170982, 784866, 3623326, 16879640, 78965889, 371797947, 1756213725, 8335157567, 39660909579, 189405764982, 906414415367, 4350153987934, 20913639508721, 100775558575863, 486305001210289, 2351158641458940, 11381247702362433, 55179764580772287, 267812212122830377

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A150556 A150557 A150558 * A150560 A150561 A122871

Adjacent sequences: A150556 A150557 A150558 * A150560 A150561 A150562

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved