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A002881 Number of simple imperfect squared rectangles of order n up to symmetry.
(Formerly M4614 N1969)
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 9, 34, 104, 283, 953, 3029, 9513, 30359, 98969, 323646, 1080659, 3668432, 12608491 (list; graph; refs; listen; history; text; internal format)



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. A squared rectangle is simple if it does not contain a smaller squared rectangle. The order of a squared rectangle is the number of constituent squares. [Geoffrey H. Morley, Oct 17 2012]


C. J. Bouwkamp, personal communication.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

W. T. Tutte, Squaring the Square, in M. Gardner's 'Mathematical Games' column in Scientific American 199, Nov. 1958, pp. 136-142, 166, Reprinted with addendum and bibliography in the US in M. Gardner, The 2nd Scientific American Book of Mathematical Puzzles & Diversions, Simon and Schuster, New York (1961), pp. 186-209, 250 [sequence on p. 207], and in the UK in M. Gardner, More Mathematical Puzzles and Diversions, Bell (1963) and Penguin Books (1966), pp. 146-164, 186-7 [sequence on p. 162].


Table of n, a(n) for n=1..24.

S. E. Anderson, Simple Imperfect Squared Rectangles [Nonsquare rectangles only.]

S. E. Anderson, Simple Imperfect Squared Squares

C. J. Bouwkamp, A. J. W. Duijvestijn and P. Medema, Tables relating to simple squared rectangles of orders nine through fifteen, Technische Hogeschool, Eindhoven, The Netherlands, August 1960, ii + 360 pp. Reprinted in EUT Report 86-WSK-03, January 1986. [Sequence p. i.]

C. J. Bouwkamp & N. J. A. Sloane, Correspondence, 1971

Eric Weisstein's World of Mathematics, Perfect Rectangle

Index entries for squared rectangles

Index entries for squared squares


a(n) = A002962(n) + A220165(n).


Cf. A006983, A002962, A002839, A220165

Cf. A181735, A217153, A217154, A217156.

Sequence in context: A147691 A000441 A067989 * A268803 A250652 A005344

Adjacent sequences:  A002878 A002879 A002880 * A002882 A002883 A002884




N. J. A. Sloane.


Stuart E Anderson, Mar 09 2011: included 'simple' in the definition, corrected terms a(13), a(15), a(16), a(17), a(18) and extended terms to a(20), gave a definition of 'simple' in the comments.

Stuart E Anderson, Apr 10 2011: Corrected a(16) to a(20), excess compounds removed.

Sequence reverted to the one in Bouwkamp et al. (1960), Gardner (1961), Sloane (1973), and Sloane & Plouffe (1995), which includes simple imperfect squares, by Geoffrey H. Morley, Oct 17 2012

Corrected a(19), a(20) extended a(21), a(22), a(23), a(24) by Stuart E Anderson, Dec 03 2012



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