A217375 Number of trivially compound perfect squared rectangles of order n up to symmetries of the rectangle.

0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 40, 168, 604, 2076, 7320, 26132, 93352, 333992, 1199716, 4329180

Offset: 1

Author

Geoffrey H. Morley, Oct 02 2012

Keywords

• nonn
• hard
• more

Comments

A squared rectangle 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. [A217153 up to a(18).]
• Index entries for squared rectangles

Crossrefs

Cf. A217374 (counts symmetries of squared subrectangles as equivalent).

Cf. A217154.

Formula

a(n) >= 2*a(n-1) + 4*A002839(n-1) + 4*A217153(n-1), with equality for n<19.

Extensions

a(20) corrected by Geoffrey H. Morley, Oct 12 2012