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A030228 Number of chiral polyominoes with n cells.

%I A030228 #50 Apr 15 2023 14:34:07
%S A030228 0,0,0,0,2,6,25,88,335,1215,4534,16823,63159,237679,900341,3423201,
%T A030228 13073163,50095285,192599091,742576616,2870584814,11122879867,
%U A030228 43191525139,168046317330,654998425237,2557224396342,9999083912711,39153000738695,153511081627903
%N A030228 Number of chiral polyominoes with n cells.
%C A030228 For n>0, A000105(n) + a(n) = A000988(n) because the number of free polyominoes plus the number of polyominoes lacking bilateral symmetry equals the number of one-sided polyominoes. - _Graeme McRae_, Jan 05 2006
%C A030228 For n>0, each chiral pair is counted as one. - _Robert A. Russell_, Feb 23 2022
%H A030228 John Mason, <a href="/A030228/b030228.txt">Table of n, a(n) for n = 0..50</a> (terms 1..45 from Andrew Howroyd, 46..48 from Robert A. Russell)
%H A030228 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 A030228 For n>0, a(n) = A000988(n) - A000105(n). - _Graeme McRae_, Jan 05 2006
%F A030228 a(n) = A006749(n) + A006747(n) + A144553(n). - _Andrew Howroyd_, Dec 04 2018
%F A030228 a(n) = A000105(n) - A030227(n). - _Robert A. Russell_, Feb 02 2019
%F A030228 For n>0, (A000988(n) - A030227(n)) / 2. - _Robert A. Russell_, Feb 23 2022
%e A030228 For a(4)=2, the two chiral tetrominoes are XXX and XX .
%e A030228                                            X        XX
%t A030228 A000105 = Cases[Import["https://oeis.org/A000105/b000105.txt", "Table"], {_, _}][[All, 2]];
%t A030228 A000988 = Cases[Import["https://oeis.org/A000988/b000988.txt", "Table"], {_, _}][[All, 2]];
%t A030228 a[n_] := A000988[[n]] - A000105[[n + 1]];
%t A030228 Array[a, 45] (* _Jean-François Alcover_, Sep 08 2019, after _Graeme McRae_ *)
%Y A030228 Cf. A000988 (oriented), A000105 (unoriented), A030227 (achiral).
%Y A030228 Cf. A006747, A006749, A144553 (subcategories).
%K A030228 nonn
%O A030228 0,5
%A A030228 _David W. Wilson_
%E A030228 Terms a(23) and beyond from _Andrew Howroyd_, Dec 04 2018
%E A030228 Name edited by _Robert A. Russell_, Feb 03 2019
%E A030228 a(0)=0 corrected by _John Mason_, Jan 12 2023