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

1,14

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

Table of n, a(n) for n=1..19.

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.

Sequence in context: A001926 A213749 A085385 * A081193 A250722 A250776

Adjacent sequences: A217149 A217150 A217151 * A217153 A217154 A217155

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