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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 (list; graph; refs; listen; history; text; internal format)
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 = 31-38 and 40-44 are from J. B. Williams. Those for n = 39 and 45-47 are from Gambini's thesis. - Geoffrey H. Morley, Mar 08 2013

======================================

Upper bounds for a(n) for n = 31 to 59

======================================

   |  +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

======================================================

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 Aix-Marseille II, 1999, pp. 73-78.

Eric Weisstein's World of Mathematics, Perfect Square Dissection

CROSSREFS

Cf. A129947, A174386, A181735, A217149, A217156.

Sequence in context: A010032 A190026 A129947 * A223822 A262521 A096680

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

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Last modified April 24 09:21 EDT 2017. Contains 285338 sequences.