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A217149 Largest possible side length for a perfect squared square of order n; or 0 if no such square exists. 3
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 (list; graph; refs; listen; history; text; internal format)



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 33 is simple.

a(30) has a lower bound of 2710. a(31) to a(33) have lower bounds of 3443, 4611 and 5976 respectively (from J. B. Williams). - Geoffrey H. Morley, Jan 10 2013


Table of n, a(n) for n=1..32.

S. E. Anderson, Perfect Squared Rectangles and Squared Squares.

Stuart Anderson, 'Special' Perfect Squared Squares", accessed 2014. - N. J. A. Sloane, Mar 30 2014

Eric Weisstein's World of Mathematics, Perfect Square Dissection


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

Sequence in context: A157662 A095615 A061281 * A119684 A235887 A211444

Adjacent sequences:  A217146 A217147 A217148 * A217150 A217151 A217152




Geoffrey H. Morley, Sep 27 2012


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



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Last modified May 27 10:03 EDT 2017. Contains 287204 sequences.