# [seqfan] Re: A sequence from the T-square fractal: help

drew at math.mit.edu drew at math.mit.edu
Wed Mar 18 12:20:37 CET 2009

```I may misunderstand you, but applying your definition to the figures in the
wikipedia entry I count

4,20,76,260,844,...

The recurrence is a(0)=0 and a(n+1)=3a(n)+2^(n+2).

Regards,

Drew

On Mar 18 2009, Simone Severini wrote:

>Dear Seqfans,
>
>I would like to know more about the following sequence:
>
>4,24,80,248,768,...
>
>Assuming that I got these numbers right, the sequence arises in the
>following way.
>
>Consider the T-square fractal polygon.
>
>See, for example,
>
>http://en.wikipedia.org/wiki/T-Square_(fractal)
>
>(The figure is very useful.)
>
> Assume that at every iteration the polygon is drawn on the integer
> lattice Z^2.
>
>It follows that the minimum length of its sides is always one.
>
>The sequence should count the number of (one by one) lattice squares
>sharing at least one side with the polygon.
>
>I hope this is clear.
>
>I would find really useful a formula for the above sequence.
>
>Thank you,
>Simone
>

```