A217153 Number of nontrivially compound perfect squared rectangles of order n up to symmetries of the rectangle.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 48, 264, 1256, 5396, 22540, 92060, 370788

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

Crossrefs

Cf. A217152 (counts symmetries of squared subrectangles as equivalent).

Cf. A002839, A181340, A217154, A217155.

Extensions

a(19) and a(20) corrected (thanks to Stuart E Anderson's computations which show I misinterpreted Gambini's counts) by Geoffrey H. Morley, Oct 12 2012