A150015 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, 0), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 5, 18, 66, 240, 960, 3868, 15717, 66099, 278019, 1184631, 5122091, 22145476, 96822325, 426006332, 1877617552, 8342165233, 37163619077, 166066819583, 745941334923, 3355458551285, 15145356845178, 68575254267863, 310903375989401, 1413892090253073, 6441832176113612, 29393857347481750

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, 1 + j, 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: A360185 A084518 A150014 * A150016 A150017 A150018

Adjacent sequences: A150012 A150013 A150014 * A150016 A150017 A150018

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved