A150211 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, -1, 1), (1, 1, 0)}.

1, 2, 6, 21, 81, 326, 1370, 5901, 25906, 115508, 521092, 2373802, 10901487, 50404116, 234397483, 1095491168, 5142163647, 24229212446, 114550696414, 543203132012, 2582844552928, 12310936486749, 58808737375853, 281491475114719, 1349853857526866, 6483971880382405, 31193982900778430, 150288210566237496

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + 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: A150209 A150210 A148492 * A148493 A148494 A150212

Adjacent sequences: A150208 A150209 A150210 * A150212 A150213 A150214

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved