[seqfan] Sphere stacks on a triangular base

[David Scambler]

Start with a layer of spheres closely packed in an equilateral triangle of side n >= 1. Add spheres by resting them
in any of the hollows between three touching spheres in the layer below. Continue until no more sites are available.

The number of stacks that can be built is

a(n) = 1, 1, 2, 9, 76, 1134, 33464, 1951187, ...

Starting with a rhombus (diamond) of side n,

a(n) =  1, 2, 9, 154, 11358, 3235665, ...

These were enumerated by a brute force algorithm that runs out of steam after a small number of terms.

Cheers
dave