A217374 Number of trivially 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, 4, 16, 60, 194, 622, 2128, 7438, 25852, 90266, 317350, 1127800

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

• C. J. Bouwkamp, On the dissection of rectangles into squares (Papers I-III), Koninklijke Nederlandsche Akademie van Wetenschappen, Proc., Ser. A, Paper I, 49 (1946), 1176-1188 (=Indagationes Math., v. 8 (1946), 724-736); Paper II, 50 (1947), 58-71 (=Indagationes Math., v. 9 (1947), 43-56); Paper III, 50 (1947), 72-78 (=Indagationes Math., v. 9 (1947), 57-63). [Paper I has terms up to a(13) on p. 1178.]
• C. J. Bouwkamp, On the construction of simple perfect squared squares, Koninklijke Nederlandsche Akademie van Wetenschappen, Proc., Ser. A, 50 (1947), 1296-1299 (=Indagationes Math., v. 9 (1947), 622-625).
• Index entries for squared rectangles

Crossrefs

Cf. A217375 (counts symmetries of squared subrectangles as distinct).

Cf. A110148.

Formula

a(n) = a(n-1) + 2*A002839(n-1) + 2*A217152(n-1).

Extensions

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