A217149 Largest possible side length for a perfect squared square of order n; or 0 if no such square exists.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 192, 332, 479, 661, 825, 1179, 1544, 2134, 2710, 3641, 4988, 6391, 8430, 11216, 15039, 20242

Offset: 1

Author

Geoffrey H. Morley, Sep 27 2012

Keywords

• nonn
• hard
• more

Comments

A squared rectangle (which may be a square) is a rectangle dissected into a finite number, two or more, of squares. If no two of these squares have the same size the squared rectangle is perfect. The order of a squared rectangle is the number of constituent squares. By convention the sides of the subsquares are integers with no common factor.

A squared rectangle is simple if it does not contain a smaller squared rectangle. Every perfect square with the largest known side length for each order up to 37 is simple.

Links

• S. E. Anderson, Perfect Squared Rectangles and Squared Squares.
• Stuart Anderson, 'Special' Perfect Squared Squares", accessed 2014. - _N. J. A. Sloane_, Mar 30 2014
• Ed Pegg Jr., Advances in Squared Squares, Wolfram Community Bulletin, Jul 23 2020
• Eric Weisstein's World of Mathematics, Perfect Square Dissection

Crossrefs

Cf. A006983, A089047, A129947, A181735, A217148, A217156.

Extensions

a(29) from Stuart E Anderson added by Geoffrey H. Morley, Nov 23 2012

a(30), a(31), a(32) from Lorenz Milla and Stuart E Anderson, added by Stuart E Anderson, Oct 05 2013

For additional terms see the Ed Pegg link, also A006983. - N. J. A. Sloane, Jul 29 2020

a(33) to a(37) from J. B. Williams added by Stuart E Anderson, Oct 27 2020