# [seqfan] Re: confused about toothpick sequence A139250!

David Wilson dwilson at gambitcomm.com
Thu Apr 16 18:42:37 CEST 2009

```a(n) = 1 + 4*SUM(k = 1 to n, 3^(A120(k)-1))

Richard Mathar wrote:
> ftaw> franktaw at netscape.net
> ftaw> Tue Apr 14 09:37:38 CEST 2009
> ftaw>
> ftaw> There is something rather general going on here.  Take almost any --
> ftaw> I'm not sure what to call it, the original term I learned was cellular
> ftaw> space, but that seems to be used for something else these days;
> ftaw> possibly grid; in any event, the kind of infinite graph that one runs
> ftaw> a cellular automaton on; it needs to be at least two-dimensional --
> ftaw> and start with a single cell in the on position.  At each step, each
> ftaw> cell with exactly one neighbor on is turned on, and everything that
> ftaw> is already on remains on.  You get this same pattern, where it shuts
> ftaw> down to a bounded number of new cells on every 2^n steps.
> ftaw> (You get some nice patterns that way, too.)
> ftaw> <snibble>
>
> I think this defines a total number of cells "on" as
> 1,5,9,21,25,37,49,85,89,101,113,149,161,197,233,341,345,357,369,...
>

```