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

1,25

Links

Table of n, a(n) for n=1..29.

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

Example

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).

Crossrefs

Cf. A217150.

Sequence in context: A169838 A249271 A272439 * A081255 A005371 A210739

Adjacent sequences: A217148 A217149 A217150 * A217152 A217153 A217154

Keyword

nonn,hard

Author

Geoffrey H. Morley, Sep 27 2012

Status

approved