A148312 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), (-1, 1, 0), (0, 1, 1), (1, -1, -1)}.

1, 1, 2, 5, 14, 37, 116, 370, 1183, 3971, 13628, 46960, 166220, 595358, 2147833, 7868630, 29023310, 107874868, 404840947, 1527363806, 5798828595, 22158950502, 85027989852, 328009874266, 1271293331349, 4944948761677, 19315800358973, 75715549901760, 297726066687929, 1174749905715126, 4648439323634846

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[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, 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: A148309 A148310 A148311 * A148313 A228952 A172259

Adjacent sequences: A148309 A148310 A148311 * A148313 A148314 A148315

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved