A217152 Number of nontrivially compound perfect squared rectangles of order n up to symmetries of the rectangle and its subrectangles.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 9, 46, 191, 781, 3161, 15002

Offset: 1

Author

Geoffrey H. Morley, Sep 27 2012

Keywords

• nonn
• hard
• more

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.]
• Index entries for squared rectangles
• Index entries for squared squares

Crossrefs

Cf. A217153 (counts symmetries of subrectangles as distinct).

Cf. A002839, A110148, A181340, A217154, A217155.

Extensions

a(18) and a(19) added by Geoffrey H. Morley, Oct 12 2012