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A217148
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Smallest possible side length for a perfect squared square of order n; or 0 if no such square exists.
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3
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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, 233, 218, 225, 253, 237
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OFFSET
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1,21
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COMMENTS
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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 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
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Upper bounds for a(n) for n = 31 to 59
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| +0 +1 +2 +3 +4 +5 +6 +7 +8 +9
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30 | - - - - - - - - 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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The sequence A129947 has identical terms to A217148 (so far), however they are different as A129947 refers to simple perfect squared squares (SPSSs), while A217148 refers to SPSSs and compound perfect squared squares (CPSSs). The simples and compounds together are referred to as perfect squared squares (PSSs). So far it has been observed that all the smallest side lengths belong to SPSSs only. - Stuart E Anderson, Oct 27 2020
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LINKS
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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