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%I #46 Apr 15 2023 12:27:09
%S 1,1,1,3,3,7,8,25,25,82,85,302,307,1111,1131,4216,4267,16076,16253,
%T 61976,62475,239927,241447,933576,937574,3644073,3653624,14267757,
%U 14281711,55996279,55968648,220244340,219829297,867868410,865120447,3425522409,3410557920,13540713898,13466370893,53596553368
%N Number of polyominoes with n cells whose symmetry group (excluding reflections) has order at least 2.
%C In other words, a(n) is the number of polyominoes with n cells having at least 180-degree rotational symmetry. - _John Mason_, Feb 14 2022
%H John Mason, <a href="/A144554/b144554.txt">Table of n, a(n) for n = 1..50</a>
%H Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/animals.html">Enumeration of polyominoes</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 D. H. Redelmeier, <a href="/A056877/a056877.png">Table 3</a> of Counting polyominoes...
%F This is the sum of A142886, A056877, A144553, A056878 and A006747. - Joseph Myers, Dec 31 2008
%F a(n) = A000105(n) - A006749(n) - A006746(n) - A006748(n). - _John Mason_, Feb 14 2022
%t A000105 = Cases[Import["https://oeis.org/A000105/b000105.txt", "Table"], {_, _}][[All, 2]];
%t A006749 = Cases[Import["https://oeis.org/A006749/b006749.txt", "Table"], {_, _}][[All, 2]];
%t A006746 = Cases[Import["https://oeis.org/A006746/b006746.txt", "Table"], {_, _}][[All, 2]];
%t A006748 = Cases[Import["https://oeis.org/A006748/b006748.txt", "Table"], {_, _}][[All, 2]];
%t a[n_] := A000105[[n+1]] - A006749[[n]] - A006746[[n]] - A006748[[n]];
%t Table[a[n], {n, 1, 48}] (* _Jean-François Alcover_, Aug 17 2022 *)
%Y Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554.
%K nonn
%O 1,4
%A _Fred Schneider_, Dec 28 2008
%E Edited by _N. J. A. Sloane_, Jan 01 2009
%E 17 additional terms (just summing the terms from the 5 sequences specified in the description) _Fred Schneider_, Jan 03 2009
%E a(28) from _John Mason_, Oct 05 2021
%E a(29)-a(36) from _John Mason_, Oct 16 2021
%E Terms a(37) and beyond from _John Mason_, Feb 14 2022
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