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%I #18 Apr 02 2014 04:46:47
%S 0,0,0,2,2,24,36,344,504,7657,11978,289829
%N Number of ways to cut an n X n square into squares with integer sides, reduced for symmetry, where the orbits under the symmetry group of the square, D4, have 2 elements.
%H Christopher Hunt Gribble, <a href="/A226978/a226978.txt">C++ program for A226978, A226979, A226980, A226981, A227004</a>
%H Ed Wynn, <a href="http://arxiv.org/abs/1308.5420">Exhaustive generation of Mrs Perkins's quilt square dissections for low orders</a>, arXiv:1308.5420
%F A226978(n) + A226979(n) + A226980(n) + A226981(n) = A224239(n).
%F 1*A226978(n) + 2*A226979(n) + 4*A226980(n) + 8*A226981(n) = A045846(n).
%F A226979(n) = A240120(n) + A240121(n) + A240122(n).
%e For n=5, there are 2 dissections where the orbits under the symmetry group of the square, D4, have 2 elements.
%e For n=4, the 2 dissections can be seen in A240120 and A240121.
%Y Cf. A045846, A034295, A219924, A224239, A226978, A226980, A226981, A240120, A240121, A240122.
%K nonn,more
%O 1,4
%A _Christopher Hunt Gribble_, Jun 25 2013
%E a(8)-a(12) from _Ed Wynn_, Apr 01 2014
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