%I #10 Jun 07 2019 19:35:06
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,1,4,7,25
%N Number of sets of n unequal squares that tile a square in exactly two ways.
%H S. E. Anderson, <a href="http://squaring.net/sq/sr/spsr/spsr_isomer.html">Simple Perfect Squared Rectangles with Isomers</a>.
%H C. J. Bouwkamp, <a href="https://doi.org/10.1016/0012-365X(92)90531-J">On some new simple perfect squared squares</a>, Discrete Math. 106-107 (1992), 67-75.
%H A. J. W. Duijvestijn, <a href="https://doi.org/10.1090/S0025-5718-1994-1208220-9">Simple perfect squared squares and 2x1 squared rectangles of order 25</a>, Math. Comp. 62 (1994), 325-332.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectSquareDissection.html">Perfect Square Dissection</a>
%e See MathWorld link for an explanation of Bouwkamp code used in this example.
%e a(26) = 1 as there is only one pair of squared squares whose 26 unequal squares can be arranged in exactly two ways. These 456x456 squared squares have Bouwkamp code (231,225)(111,114)(126,105)(35,58,120,3)(117)(99,27)(12,23)(1,11)(18,10)(8,32,62)(26)(2,30)(28) and (231,225)(111,114)(126,105)(35,58,120,3)(117)(99,27)(12,23)(1,11)(28)(30,62)(18,10)(8,2)(32)(26).
%Y Cf. A217150.
%K nonn,hard
%O 1,25
%A _Geoffrey H. Morley_, Sep 27 2012