A150564 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, 0, 0), (0, -1, 1), (0, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 26, 107, 455, 1997, 8943, 40724, 187692, 873596, 4098024, 19348509, 91843291, 437942044, 2096335325, 10068086873, 48493635634, 234162526076, 1133219494555, 5494968832105, 26691822562948, 129859549681074, 632680348401466, 3086391197803401, 15073802311868993, 73697945585736510

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[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A122871 A150562 A150563 * A150565 A150566 A150567

Adjacent sequences: A150561 A150562 A150563 * A150565 A150566 A150567

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved