A149232 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, 0), (0, 0, -1), (1, 1, 1)}.

1, 1, 4, 11, 32, 110, 360, 1163, 4112, 14066, 47848, 171382, 601488, 2101436, 7600784, 27098643, 96279392, 350734058, 1264010472, 4542868898, 16640111312, 60442510244, 219059021360, 805881760158, 2944834666144, 10741157899508, 39654320911760, 145590617001804, 533710778498976, 1976115749381496

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A025268 A178520 A306419 * A149233 A273038 A179905

Adjacent sequences: A149229 A149230 A149231 * A149233 A149234 A149235

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved