A151218 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, 0, 1), (1, 1, 0), (1, 1, 1)}.

1, 3, 13, 55, 263, 1196, 5850, 27528, 135726, 650470, 3222016, 15609182, 77539788, 378324161, 1882662003, 9231694688, 45993117480, 226350480727, 1128618140674, 5569574647042, 27787141854434, 137415451974877, 685877545678394, 3397519340596185, 16963524419041184, 84141927427400882

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, -1 + j, k, -1 + n] + aux[-1 + i, 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: A151215 A151216 A151217 * A151219 A006225 A100588

Adjacent sequences: A151215 A151216 A151217 * A151219 A151220 A151221

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved