A151236 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, 1, 0), (1, 0, 0), (1, 1, 0), (1, 1, 1)}.

1, 3, 14, 59, 288, 1311, 6489, 30535, 151900, 727661, 3627957, 17569091, 87696862, 427745087, 2136486736, 10473195599, 52331021438, 257470685339, 1286792210593, 6348564659473, 31733612417336, 156896784297081, 784330025193552, 3884420348128291, 19419492138511104, 96306261946366663

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + 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: A319857 A038679 A151235 * A006224 A219544 A131262

Adjacent sequences: A151233 A151234 A151235 * A151237 A151238 A151239

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved