A110148 Number of perfect squared rectangles of order n up to symmetries of the rectangle and of its subrectangles if any.

0, 0, 0, 0, 0, 0, 0, 0, 2, 10, 38, 127, 408, 1375, 4783, 16645, 58059, 203808, 722575

Offset

1,9

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. [Geoffrey H. Morley, Oct 12 2012]

Links

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

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(12) and an incorrect value for 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). [Correct terms up to a(13) on p. 1299.]

I. M. Yaglom, How to dissect a square? (in Russian), Nauka, Moscow, 1968. In djvu format (1.7M), also as this pdf (9.5M). [Terms up to a(13) on pp. 26-7.]

Index entries for squared rectangles

Index entries for squared squares

Formula

a(n) = A002839(n) + A217152(n) + A217374(n). - Geoffrey H. Morley, Oct 12 2012

a(n) = a(n-1) + A002839(n) + A002839(n-1) + A217152(n) + A217152(n-1). - Geoffrey H. Morley, Oct 12 2012

Crossrefs

Cf. A217154 (counts symmetries of any subrectangles as distinct).

Cf. A181735, A217153, A217156.

Sequence in context: A046241 A048499 A119358 * A281199 A081956 A056182

Adjacent sequences: A110145 A110146 A110147 * A110149 A110150 A110151

Keyword

nonn,hard,more

Author

Tanya Khovanova, Feb 18 2007

Extensions

Definition corrected and a(14)-a(19) added by Geoffrey H. Morley, Oct 12 2012

Status

approved