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A217154
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Number of 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, 2, 14, 62, 235, 821, 2868, 10193, 36404, 130174, 466913, 1681999, 6083873
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OFFSET
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1,9
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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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REFERENCES
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See crossrefs for references and links.
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LINKS
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FORMULA
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EXAMPLE
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a(10) = 14 comprises the A002839(10) = 6 simple perfect squared rectangles (SPSRs) of order 10 and the 8 trivially compound perfect squared rectangles which each comprises one of the two order 9 SPSRs and one other square.
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CROSSREFS
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Cf. A110148 (counts symmetries of any 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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