A151177 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), (1, 0, 0), (1, 0, 1), (1, 1, 1)}

1, 3, 12, 49, 224, 1003, 4795, 22343, 108701, 517169, 2539693, 12239287, 60428125, 293673869, 1454899827, 7112278267, 35315525591, 173378316769, 862262869950, 4246791976980, 21144661336751, 104398733451674, 520236235063489, 2573592946206401, 12832805881033345, 63582494681839206, 317199347679668932

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, j, 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: A151174 A151175 A151176 * A344419 A002179 A224659

Adjacent sequences: A151174 A151175 A151176 * A151178 A151179 A151180

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved