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%I M4614 N1969 #42 Oct 21 2023 01:14:19
%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 its 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, 186-187 [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 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
%E a(16)-a(20) corrected (excess compounds removed) by _Stuart E Anderson_, Apr 10 2011
%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 a(19)-a(20) corrected, a(21)-a(24) added by _Stuart E Anderson_, Dec 03 2012
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