cp's OEIS Frontend

A226978 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 1 element.

%I A226978 #30 Dec 15 2022 10:00:30
%S A226978 1,2,2,4,4,12,8,44,32,228,148,1632,912,16004,8420,213680,101508,
%T A226978 3933380,1691008,98949060,38742844,3413919788,1213540776,161410887252,
%U A226978 52106993880
%N A226978 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 1 element.
%C A226978 From _Walter Trump_, Dec 15 2022: (Start)
%C A226978 a(n) is the number of fully symmetric dissections of an n X n square into squares with integer sides.
%C A226978 Conjecture: For n>3 the number of dissections is a multiple of 4. (End)
%H A226978 Christopher Hunt Gribble, <a href="/A226978/a226978.txt">C++ program for A226978, A226979, A226980, A226981, A227004</a>
%H A226978 Walter Trump, <a href="/A226978/a226978.png">Example for n=19</a>
%F A226978 a(n) + A226979(n) + A226980(n) + A226981(n) = A224239(n).
%F A226978 1*a(n) + 2*A226979(n) + 4*A226980(n) + 8*A226981(n) = A045846(n).
%e A226978 For n=5, there are 4 dissections where the orbits under the symmetry group of the square, D4, have 1 element.
%e A226978 For n=4, 3 dissections divide the square into uniform subsquares (of sizes 1, 2 and 4 respectively), and this is the 4th:
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%Y A226978 Cf. A045846, A034295, A219924, A224239, A226979, A226980, A226981.
%K A226978 nonn,more
%O A226978 1,2
%A A226978 _Christopher Hunt Gribble_, Jun 25 2013
%E A226978 a(8)-a(12) from _Ed Wynn_, Apr 02 2014
%E A226978 a(13)-a(25) from _Walter Trump_, Dec 15 2022