A150255 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), (0, 1, -1), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 6, 22, 86, 340, 1403, 5912, 25255, 109518, 478944, 2112598, 9392174, 41972854, 188575186, 851123779, 3855663703, 17529454105, 79937906002, 365518321803, 1675610232396, 7698292434046, 35440859672787, 163468742882547, 755269073235057, 3495106155974599, 16197749380386370, 75168376975945930

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[i, -1 + j, 1 + 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: A116707 A116704 A029759 * A107243 A107244 A107245

Adjacent sequences: A150252 A150253 A150254 * A150256 A150257 A150258

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved