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A001933 Number of chessboard polyominoes with n squares.

%I A001933 M0171 N0066 #59 Dec 23 2024 14:53:41
%S A001933 2,1,4,7,24,62,216,710,2570,9215,34146,126853,477182,1802673,6853152,
%T A001933 26153758,100215818,385226201,1485248464,5741275753,22246121356,
%U A001933 86383454582,336094015456,1309998396933,5114454089528,19998173763831,78306021876974,307022186132259,1205243906123956,4736694016531135
%N A001933 Number of chessboard polyominoes with n squares.
%C A001933 Chessboard-colored polyominoes, considering to be distinct two shapes that cannot be mapped onto each other by any form of symmetry. For example, there are two distinct monominoes, one black, one white. There is only one domino, with one black square, and one white. - _John Mason_, Nov 25 2013
%D A001933 W. F. Lunnon, personal communication.
%D A001933 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001933 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001933 John Mason, <a href="/A001933/b001933.txt">Table of n, a(n) for n = 1..50</a>
%H A001933 Joseph Myers, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2010-November/013893.html">Chessboard polyominoes</a>
%F A001933 For odd n, a(n) = 2*A000105(n).
%F A001933 For n multiple of 2 but not of 4, a(n) = 2*A000105(n) - (A234006(n/2) + A234008(n/2)).
%F A001933 For n multiple of 4, a(n) = 2*A000105(n) - (A234006(n/2) + A234008(n/2) + A234007(n/4)). - _John Mason_, Dec 23 2021
%Y A001933 Cf. A001071, A000105, A121198, A234006 (free polyominoes of size 2n that have at least reflectional symmetry on a horizontal or vertical axis that coincides with the edges of some of the squares), A234007 (free polyominoes with 4n squares, having 90-degree rotational symmetry about a square corner, but not having reflective symmetry), A234008 (free polyominoes with 2n squares, having 180-degree rotational symmetry about a square mid-side, but no reflective symmetry).
%K A001933 hard,nonn
%O A001933 1,1
%A A001933 _N. J. A. Sloane_
%E A001933 a(14)-a(17) from _Joseph Myers_, Oct 01 2011
%E A001933 a(18)-a(23) from _John Mason_, Dec 05 2013
%E A001933 a(24)-a(30) from _John Mason_, Dec 23 2021