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%I #20 Jan 21 2023 03:05:24
%S 0,1,0,1,1,3,3,9,13,35,59,147,280,669,1347,3142,6545,15110,32057,
%T 73625,158056,362280,783800,1795134,3906573,8946154,19558340
%N Number of unoriented polyomino rings of length 2n with twofold rotational symmetry.
%C This sequence and its chiral and achiral versions correspond to Robert A. Russell's similar sequences for rings of fourfold rotational symmetry. The sequence does not count the mononimo or domino, referred to by Redelmeier as degenerate rings, as they are not in fact rings.
%C The sequence refers to rings with at least twofold (180-degree) rotational symmetry, and so includes those with (i) fourfold (90-degree) rotational symmetry, and (ii) all symmetries. - _John Mason_, Jan 19 2023
%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.
%F a(n) = A348403(n) + A348404(n).
%e a(2)=1 because of:
%e OO
%e OO
%e a(4)=1 because of:
%e OOO
%e O.O
%e OOO
%e a(5)=1 because of:
%e OOOO
%e O..O
%e OOOO
%Y Cf. A348403 (chiral), A348404 (achiral), A324407 (unoriented with fourfold rotational symmetry), A324408 (chiral with fourfold rotational symmetry), A324409 (achiral with fourfold rotational symmetry).
%K nonn,more
%O 1,6
%A _John Mason_, Oct 18 2021
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