A150319 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), (-1, 1, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 21, 91, 327, 1484, 5675, 26890, 108150, 518000, 2134639, 10387785, 43812503, 214054127, 914666899, 4502498672, 19496286492, 96142162678, 419739091653, 2078335033029, 9151746372466, 45355128693029, 200858769671480, 997852654448529, 4445683777700944, 22096455282317883, 98861664473092120

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, j, k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A150316 A150317 A150318 * A150320 A150321 A076716

Adjacent sequences: A150316 A150317 A150318 * A150320 A150321 A150322

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved