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 A324408 #9 Sep 30 2021 22:12:48
%S A324408 0,0,0,0,1,2,6,12,29,61,138,294,649,1402,3073,6696,14676,32199,70764,
%T A324408 156062,344209,762433,1687745,3751845,8333371,18582147,41399110,
%U A324408 92557961,206765077,463343343,1037518525,2329710014,5227630580,11759537552,26436259384
%N A324408 Number of chiral pairs of polyomino rings of length 4n with fourfold rotational symmetry.
%C A324408 Redelmeier uses these rings to enumerate polyominoes of the regular tiling {4,4} with fourfold rotational symmetry (A144553) and an even number of cells. Each cell of a polyomino ring is adjacent to (shares an edge with) exactly two other cells. Each chiral ring is congruent to but different from its reflection; the two form a chiral pair.
%C A324408 These chiral rings have fourfold symmetry.
%C A324408 For n odd, the center of the ring is a vertex of the tiling; for n even, the center is the center of a tile.
%C A324408 In early September, 2021, _John Mason_ informed me that a(16) should be 6696 instead of 6695. He supplied me with representations of all of the rings, and I slowly discovered that my program had missed one and had serious errors. After I corrected it, we did match new values for a(16), a(18), a(20), and a(22). We are reasonably confident that the values shown are now correct. - _Robert A. Russell_, Sep 30 2021
%H A324408 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.
%F A324408 a(n) = A324406(n) - A324407(n) = (A324406(n) - A324409(n)) / 2 = A324407(n) - A324409(n).
%e A324408 For a(5) = 1, the pair is XXX XXX .
%e A324408 X XXX XXX X
%e A324408 XX X X XX
%e A324408 X XX XX X
%e A324408 XXX X X XXX
%e A324408 XXX XXX
%Y A324408 Cf. A324406 (oriented), A324407 (unoriented), A324409 (achiral).
%Y A324408 Cf. also A144553.
%K A324408 nonn,hard
%O A324408 1,6
%A A324408 _Robert A. Russell_, Feb 26 2019