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%I #13 Dec 04 2021 12:43:48
%S 1,2,6,19,65,224,790,2851,10424,38496,143454,538667,2035180,7729146,
%T 29486904,112942373,434114384,1673766428,6471199322,25081542410,
%U 97431694571,379256586232,1479022885116
%N Number of oriented polyominoes with 4n cells that have fourfold rotational symmetry centered at a vertex.
%C These are polyominoes of the regular tiling with Schläfli symbol {4,4}. For oriented polyominoes, chiral pairs are counted as two. This is one of the five sequences, along with A001168, needed to calculate the number of oriented polyominoes, A000988. It is the C90(n/4) sequence in the Shirakawa link. The calculation follows Redelmeier's method of inner rings.
%H Robert A. Russell, <a href="/A348848/b348848.txt">Table of n, a(n) for n = 1..23</a>
%H D. H. Redelmeier, <a href="http://dx.doi.org/10.1016/0012-365X(81)90237-5">Counting polyominoes: yet another attack</a>, Discrete Math., 36 (1981), 191-203.
%H Toshihiro Shirakawa, <a href="https://www.gathering4gardner.org/g4g10gift/math/Shirakawa_Toshihiro-Harmonic_Magic_Square.pdf">Enumeration of Polyominoes considering the symmetry</a>, April 2012, pp. 3-4.
%e For a(1)=1, the polyomino is a 2 X 2 square. For a(2)=2, the two polyominoes are a chiral pair having a central 2 X 2 square with one cell attached to each edge of that square.
%Y Cf. A000988, A144553, A348849 (cell center).
%Y Inner rings: A324406, A324407, A324408, A324409.
%K nonn
%O 1,2
%A _Robert A. Russell_, Nov 01 2021
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