A182947 Number of complete sphere stacks on a triangular base with side length n.

1, 1, 2, 9, 76, 1134, 33464, 1951187

Offset

1,3

Comments

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.

a(n) is the number of distinct complete stacks that can be built.

Links

Table of n, a(n) for n=1..8.

Example

For n=3 there are two complete stacks, so a(3)=2.
.
  3 layers, 10 spheres        2 layers, 7 spheres
.
            1                          1
           / \                        / \
          / 2 \                      /   \
         1-----1                    1-----1
        / \ 3 / \                  / \ 2 / \
       / 2 \ / 2 \                /   \ /   \
      1-----1-----1              1-----1-----1

Crossrefs

Cf. A182948 = spheres on a rhombic base.

Sequence in context: A058164 A006059 A277406 * A006041 A192551 A121131

Adjacent sequences: A182944 A182945 A182946 * A182948 A182949 A182950

Keyword

nonn,more

Author

David Scambler, Dec 14 2010

Status

approved