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A217152 Number of nontrivially compound perfect squared rectangles of order n up to symmetries of the rectangle and its subrectangles. 5
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 9, 46, 191, 781, 3161, 15002 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,14
COMMENTS
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.
LINKS
I. Gambini, Quant aux carrés carrelés, Thesis, Université de la Méditerranée Aix-Marseille II, 1999, p. 24. [But symmetries of subrectangles counted as distinct.]
CROSSREFS
Cf. A217153 (counts symmetries of subrectangles as distinct).
Sequence in context: A001926 A213749 A085385 * A081193 A250722 A250776
KEYWORD
nonn,hard,more
AUTHOR
Geoffrey H. Morley, Sep 27 2012
EXTENSIONS
a(18) and a(19) added by Geoffrey H. Morley, Oct 12 2012
STATUS
approved

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Last modified March 19 02:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)