[seqfan] Mystery concerning sequences A169720-A169727

Neil Sloane njasloane at gmail.com
Sun Dec 2 02:58:31 CET 2012


Dear Seq Fans, Two years ago, Alice Kleeva, from the Hermitage Museum in
St Petersburg, submitted these sequences.The illustrations of the initial
terms
are some of the most beautiful figures in all of the OEIS.
But I can't find my notes on these sequences.

The question is, how are the terms of the sequences related to the drawings?

Take A169720, which begins 1, 10, 55, 253, 1081, 4465, ...,
and compare it with the "Illustration of initial terms".
Where does 10 come from? 55?

I did find some comments from Alice Kleeva, which said:

(start of quote)
Generally, I am interesting in the visualization of integer sequences. My
geometrical ornaments are correlated with numerical sequences and with
geometrical figures (hexagonal star, octagonal star and others).

The method is based on the figurate numbers of Pythagoras and on the regular
division of the plane by square and triangle grids (see pic. grid_square.jpg
and grid_triangle.jpg). The points are connected rhythmically in some way in
a regular point system (see pic. scheme1.jpg, scheme2.jpg, scheme3.jpg).
An initial geometrical figure is inscribed in a similar figure, etc. Thus we
obtain the sequence ...
(end of quote)

The figures mentioned are now attached to the eight sequences under
discussion.
But how are the sequences obtained from the drawings?

Neil


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