A150257 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, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 6, 22, 86, 353, 1495, 6502, 28743, 128758, 583451, 2668374, 12292808, 56987684, 265676183, 1244433194, 5852518906, 27624837972, 130821101228, 621293592096, 2958220122533, 14118507202472, 67526342652503, 323588154320133, 1553393724528138, 7469343363407163, 35969576972881314, 173456125461130407

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 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: A047849 A277222 A150256 * A150258 A073075 A299021

Adjacent sequences: A150254 A150255 A150256 * A150258 A150259 A150260

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved