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A217153
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Number of nontrivially compound perfect squared rectangles of order n up to symmetries of the rectangle.
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9
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 48, 264, 1256, 5396, 22540, 92060, 370788
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OFFSET
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1,13
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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, compound if it does, and trivially compound if a constituent square has the same side length as a side of the squared rectangle under consideration.
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LINKS
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I. Gambini, Quant aux carrés carrelés, Thesis, Université de la Méditerranée Aix-Marseille II, 1999, p. 24. [Number of compound rectangles includes any that comprises a square sandwiched between two rectangles (from order 19) and excludes squares in separate column (order 24).]
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CROSSREFS
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Cf. A217152 (counts symmetries of squared subrectangles as equivalent).
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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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