[seqfan] Re: a question about arrangements of pennies

John W. Layman layman at math.vt.edu
Wed Dec 16 19:34:01 CET 2009

```For n=7 in the "simpler" problem below, I get the additional configuration:

o o
o o o
o o

so it appears that a(7) is greater than or equal to 7

John

N. J. A. Sloane wrote:
> ...
> First let me state a simpler question.
>
> 1.  Take the standard triangular lattice packing
> of pennies, in which each penny touches 6 others.
> How many ways are there to pick n pennies (modulo
> rotations and reflections) such that if you construct
> the graph with nodes = centers of pennies,
> edges = pairs of touching pennies,
> then this graph is connected and every edge
> belongs to at least one triangle?
>
> Here's what I get for the first few cases:
> n  1 2 3 4 5 6 7
> #  1 0 1 1 2 3 6
>
> Here they are:
>  o
> o o
>
>  o
> o o
>  o
>
>  o o
> o o o
>
>    o
> o o o
>  o
>
> I'll skip 6
>
>  o o o
> o o o o
>
>  o o
> o o o
>  o o
>
>   o o
>  o o
> o o o
>
>    o o
> o o o o
>  o
>
>    o o
>   o o o
>  o o
>
>    o
> o o o o
>  o   o
>
>

```