A148308 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, 0, 1), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 5, 14, 37, 116, 346, 1112, 3541, 11718, 38574, 130865, 440660, 1519793, 5214004, 18188974, 63305611, 222942065, 784291208, 2784447158, 9878585955, 35305415420, 126140847292, 453298218308, 1629160701989, 5882062162040, 21245124137579, 77019547575392, 279356605426514, 1016369541881713, 3699924613202552

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[1 + i, 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: A117294 A148306 A148307 * A148309 A148310 A148311

Adjacent sequences: A148305 A148306 A148307 * A148309 A148310 A148311

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved