This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A348849 #6 Dec 04 2021 12:44:01
%S A348849 1,0,0,0,1,0,0,1,2,0,0,3,6,0,0,10,18,0,0,35,57,0,0,126,191,0,0,461,
%T A348849 658,0,0,1699,2308,0,0,6315,8241,0,0,23686,29853,0,0,89432,109268,0,0,
%U A348849 339473,403450,0,0,1294826,1501074
%N A348849 Number of fixed polyominoes with n cells that have fourfold rotational symmetry centered at the center of a cell.
%C A348849 These are polyominoes of the regular tiling with Schläfli symbol {4,4}. 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 F90 sequence in the Shirakawa link. The calculation follows Redelmeier's method of determining inner rings.
%H A348849 Robert A. Russell, <a href="/A348849/b348849.txt">Table of n, a(n) for n = 1..96</a>
%H A348849 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 A348849 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 A348849 For a(9)=2, the polyomino is a 3 X 3 square or a row and column of five cells sharing their central cells.
%Y A348849 Cf. A000988, A144553, A348848 (vertex center).
%Y A348849 Inner rings: A324406, A324407, A324408, A324409.
%K A348849 nonn
%O A348849 1,9
%A A348849 _Robert A. Russell_, Nov 01 2021