cp's OEIS Frontend

A226981 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 8 elements.

%I A226981 #20 Apr 05 2014 13:25:34
%S A226981 0,0,0,1,45,1194,55777,4471175,669049507,187616301623,98793450008033,
%T A226981 97702667035688951
%N A226981 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 8 elements.
%H A226981 Christopher Hunt Gribble, <a href="/A226978/a226978.txt">C++ program for A226978, A226979, A226980, A226981, A227004</a>
%H A226981 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 A226981 A226978(n) + A226979(n) + A226980(n) + A226981(n) = A224239(n).
%F A226981 1*A226978(n) + 2*A226979(n) + 4*A226980(n) + 8*A226981(n) = A045846(n).
%e A226981 For n=5, there are 45 dissections where the orbits under the symmetry group of the square, D4, have 8 elements.
%e A226981 For n=4, this is the only dissection:
%e A226981 ---------
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%e A226981 -----   |
%e A226981 | | |   |
%e A226981 ---------
%e A226981 | | | | |
%e A226981 ---------
%Y A226981 Cf. A045846, A034295, A219924, A224239, A226978, A226979, A226980.
%K A226981 nonn,more
%O A226981 1,5
%A A226981 _Christopher Hunt Gribble_, Jun 25 2013
%E A226981 a(8)-a(12) from _Ed Wynn_, Apr 02 2014