

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
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OFFSET

1,21


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 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


LINKS

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


CROSSREFS

Cf. A089047, A129947, A181735, A217148, A217156.
Sequence in context: A157662 A095615 A061281 * A119684 A235887 A296579
Adjacent sequences: A217146 A217147 A217148 * A217150 A217151 A217152


KEYWORD

nonn,hard


AUTHOR

Geoffrey H. Morley, Sep 27 2012


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


STATUS

approved



