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

Offset

1,12

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

References

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, 186-187 [sequence on p. 162].

Links

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

Formula

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

Crossrefs

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

Keyword

hard,nonn

Author

N. J. A. Sloane

Extensions

Edited ("simple" added to the definition, definition of "simple" given in the comments), terms a(13), a(15), a(16), a(17), and a(18) corrected, and terms extended to a(20) by Stuart E Anderson, Mar 09 2011

a(16)-a(20) corrected (excess compounds removed) by Stuart E Anderson, Apr 10 2011

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

a(19)-a(20) corrected, a(21)-a(24) added by Stuart E Anderson, Dec 03 2012

Status

approved