cp's OEIS Frontend

A226980 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 4 elements.

%I A226980 #18 Apr 01 2014 20:49:34
%S A226980 0,0,1,6,26,264,1157,23460,153485,6748424,70521609,6791578258
%N A226980 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 4 elements.
%H A226980 Christopher Hunt Gribble, <a href="/A226978/a226978.txt">C++ program for A226978, A226979, A226980, A226981, A227004</a>
%H A226980 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 A226980 A226978(n) + A226979(n) + A226980(n) + A226981(n) = A224239(n).
%F A226980 1*A226978(n) + 2*A226979(n) + 4*A226980(n) + 8*A226981(n) = A045846(n).
%F A226980 A226980(n) = A240123(n) + A240124(n) + A240125(n).
%e A226980 For n=5, there are 26 dissections where the orbits under the symmetry group of the square, D4, have 4 elements.
%e A226980 The 6 dissections for n=4 can be seen in A240123 and A240125.
%Y A226980 Cf. A045846, A034295, A219924, A224239, A226978, A226979, A226981, A240123, A240124, A240125.
%K A226980 nonn,more
%O A226980 1,4
%A A226980 _Christopher Hunt Gribble_, Jun 25 2013
%E A226980 a(8)-a(12) from _Ed Wynn_, Apr 01 2014