A217151 Number of sets of n unequal squares that tile a square in exactly two ways.

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

Offset: 1

Author

Geoffrey H. Morley, Sep 27 2012

Keywords

• nonn
• hard

Examples

			See MathWorld link for an explanation of Bouwkamp code used in this example.
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).
		

Links

• S. E. Anderson, Simple Perfect Squared Rectangles with Isomers.
• C. J. Bouwkamp, On some new simple perfect squared squares, Discrete Math. 106-107 (1992), 67-75.
• A. J. W. Duijvestijn, Simple perfect squared squares and 2x1 squared rectangles of order 25, Math. Comp. 62 (1994), 325-332.
• Eric Weisstein's World of Mathematics, Perfect Square Dissection

Crossrefs

Cf. A217150.