

A217148


Smallest 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, 110, 110, 120, 147, 212, 180, 201, 221, 201, 215, 185
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OFFSET

1,21


COMMENTS

It is not known whether this sequence is the same as sequence A129947. It may be that A129947(33) = 246 and A217148(33) = 234.  Geoffrey H. Morley, Jan 10 2013
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.
A squared rectangle is simple if it does not contain a smaller squared rectangle.
The upper bounds shown below for n = 3138 and 4044 are from J. B. Williams. Those for n = 39 and 4547 are from Gambini's thesis.  Geoffrey H. Morley, Mar 08 2013
======================================
Upper bounds for a(n) for n = 31 to 59
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 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9
======================================================
30     234 315 276 341 319 352 360
40  328 336 360 413 425 543 601 691 550 583
50  644 636 584 685 657 631 751 742 780 958
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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
I. Gambini, Quant aux carres carreles, Thesis, Universite de la Mediterranee AixMarseille II, 1999, pp. 7378.
Eric Weisstein's World of Mathematics, Perfect Square Dissection


CROSSREFS

Cf. A129947, A174386, A181735, A217149, A217156.
Sequence in context: A010032 A190026 A129947 * A223822 A300006 A262521
Adjacent sequences: A217145 A217146 A217147 * A217149 A217150 A217151


KEYWORD

nonn,hard,more


AUTHOR

Geoffrey H. Morley, Sep 27 2012


EXTENSIONS

a(29) from Stuart E Anderson added by Geoffrey H. Morley, Nov 23 2012
a(30) from Stuart E Anderson and Lorenz Milla added by Geoffrey H. Morley, Jun 15 2013
a(31) and a(32) from Lorenz Milla and Stuart E Anderson, Oct 05 2013


STATUS

approved



