A151051 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, 1, -1), (0, 0, 1), (1, 0, 0), (1, 0, 1)}.

1, 3, 10, 37, 143, 585, 2474, 10676, 46847, 208584, 940109, 4278267, 19615829, 90525966, 420246448, 1960950448, 9190034528, 43231693467, 204062350204, 966205062996, 4587557733718, 21835695015254, 104165428886620, 497936775016721, 2384782452148250, 11441368406753390, 54979295791255949

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A357399 A219260 A151050 * A164044 A119244 A151052

Adjacent sequences: A151048 A151049 A151050 * A151052 A151053 A151054

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved