A150973 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), (0, 1, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 36, 160, 716, 3314, 15388, 72499, 342935, 1635960, 7824257, 37611809, 181209322, 876049115, 4242706707, 20596344336, 100135723710, 487704113642, 2378266514902, 11613225600136, 56767518355194, 277790357624818, 1360560956453716, 6669645937906914, 32720231458322324, 160639177418874272

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, -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: A150970 A150971 A150972 * A150974 A248438 A288780

Adjacent sequences: A150970 A150971 A150972 * A150974 A150975 A150976

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved