

A110148


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


5



0, 0, 0, 0, 0, 0, 0, 0, 2, 10, 38, 127, 408, 1375, 4783, 16645, 58059, 203808, 722575
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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 IIII), Koninklijke Nederlandsche Akademie van Wetenschappen, Proc., Ser. A, Paper I, 49 (1946), 11761188 (=Indagationes Math., v. 8 (1946), 724736); Paper II, 50 (1947), 5871 (=Indagationes Math., v. 9 (1947), 4356); Paper III, 50 (1947), 7278 (=Indagationes Math., v. 9 (1947), 5763). [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), 12961299 (=Indagationes Math., v. 9 (1947), 622625). [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. 267.]
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(n1) + A002839(n) + A002839(n1) + A217152(n) + A217152(n1).  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 A056182 A081956
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



