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

Simone Severini simoseve at gmail.com
Wed Mar 18 09:06:33 CET 2009

Dear Seqfans,

I would like to know more about the following sequence:


Assuming that I got these numbers right, the sequence arises in the
following way.

Consider the T-square fractal polygon.

See, for example,


(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 Severini

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