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A002881 Number of simple imperfect squared rectangles of order n up to symmetry.
(Formerly M4614 N1969)

%I M4614 N1969

%S 0,0,0,0,0,0,0,0,1,0,0,9,34,104,283,953,3029,9513,30359,98969,323646,

%T 1080659,3668432,12608491

%N Number of simple imperfect squared rectangles of order n up to symmetry.

%C 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]

%D C. J. Bouwkamp, personal communication.

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

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

%D 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].

%H S. E. Anderson, <a href="http://www.squaring.net/sq/sr/sisr/sisr.html">Simple Imperfect Squared Rectangles</a> [Nonsquare rectangles only.]

%H S. E. Anderson, <a href="http://www.squaring.net/sq/ss/siss/siss.html">Simple Imperfect Squared Squares</a>

%H 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 <a href="http://alexandria.tue.nl/repository/books/150593.pdf">EUT Report 86-WSK-03, January 1986</a>. [Sequence p. i.]

%H C. J. Bouwkamp & N. J. A. Sloane, <a href="/A000162/a000162.pdf">Correspondence, 1971</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectRectangle.html">Perfect Rectangle</a>

%H <a href="/index/Sq#squared_rectangles">Index entries for squared rectangles</a>

%H <a href="/index/Sq#squared_squares">Index entries for squared squares</a>

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

%Y Cf. A006983, A002962, A002839, A220165

%Y Cf. A181735, A217153, A217154, A217156.

%K hard,nonn

%O 1,12

%A _N. J. A. Sloane_.

%E 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.

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

%E 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

%E 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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Last modified January 24 04:31 EST 2018. Contains 298115 sequences.