Up to symmetry, the numbers of simple perfect squared rectangles of orders 8, 9, 10, ... are 0, 2, 6, 22,
67, 213, 744, 2609, ... (OEIS A002839). The
corresponding numbers of simple imperfect squared rectangles
are 0, 1, 0, 0, 9, 34, 104, 283, ... (OEIS A002881).
These counts include squares as special cases of rectangles
(Anderson).
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C. J. "On the Dissection of Rectangles into Squares. I." Indag.
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Dissection of Rectangles into Squares. II." Indag. Math.9, 43-56,
1947.Bouwkamp, C. J. "On the Dissection of Rectangles into
Squares. III." Indag. Math.9, 57-63, 1947.Brooks,
R. L.; Smith, C. A. B.; Stone, A. H.; and Tutte, W. T. "The
Dissection of Rectangles into Squares." Duke Math. J.7, 312-340,
1940.Croft, H. T.; Falconer, K. J.; and Guy, R. K. "Squaring
the Square." §C2 in Unsolved
Problems in Geometry. New York: Springer-Verlag, pp. 81-83, 1991.Descartes,
B. "Division of a Square into Rectangles." Eureka, No. 34,
31-35, 1971.Duijvestijn, A. J. W. "Electronic Computation
of Squared Rectangles." Thesis. Eindhoven, Netherlands: Technische Hogeschool,
1962.Moroń, Z. "O rozkładach prostokatów na kwadraty."
Przeglad matematyczno-fizyczny3, 152-153, 1925.Scherer,
K. "Square the Square." http://karl.kiwi.gen.nz/prosqtsq.html.Sloane,
N. J. A. Sequences A002839/M1658
and A002881/M4614 in "The On-Line Encyclopedia
of Integer Sequences."Stewart, I. "Squaring the Square."
Sci. Amer.277, 94-96, July 1997.Wells, D. The
Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England:
Penguin Books, p. 73, 1986.Wolf, T. "The Puzzle." https://web.archive.org/web/20020111140015/http://home.tiscalinet.ch:80/t_wolf/tw/misc/squares.html.
Puzzle."