[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
>
>
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