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%I #16 Apr 20 2021 02:41:43
%S 1,1,2,9,76,1134,33464,1951187
%N Number of complete sphere stacks on a triangular base with side length n.
%C 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.
%C a(n) is the number of distinct complete stacks that can be built.
%e For n=3 there are two complete stacks, so a(3)=2.
%e .
%e 3 layers, 10 spheres 2 layers, 7 spheres
%e .
%e 1 1
%e / \ / \
%e / 2 \ / \
%e 1-----1 1-----1
%e / \ 3 / \ / \ 2 / \
%e / 2 \ / 2 \ / \ / \
%e 1-----1-----1 1-----1-----1
%Y Cf. A182948 = spheres on a rhombic base.
%K nonn,more
%O 1,3
%A _David Scambler_, Dec 14 2010
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