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 A108066 Number of distinct ways to dissect a square into n rectangles of equal area. 5
 1, 1, 2, 6, 18, 65, 281, 1343, 6953, 38023 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS "Distinct" here means that dissections differing only by a rotation and/or reflection are not counted as different (see A189243). The first time the pieces can be made to all have different shapes (but the same area) is at n=7 - see Descartes (1971) and the illustration; also Wells, Weisstein. - N. J. A. Sloane, Dec 05 2012 REFERENCES Blanche Descartes, Divisions of a square into rectangles, Eureka, No. 34 (1971), 31-35. David Wells, Penguin Dictionary of Curious and Interesting Geometry, 1991, pp. 15-16. LINKS R. Häggkvist, P.-O. Lindberg, and B. Lindström, Dissecting a square into rectangles of equal area, Discr. Math. 47 (1983), 321-323. Johan Nilsson, Illustrations for terms up to a(6). Eric Weisstein, Blanche's Dissection. EXAMPLE There are six ways to dissect a square into four rectangles of equal area, so a(4)=6: +-+-----+ +-+-+---+ +-+-----+ +-+-+-+-+ +-+---+-+ +---+---+ | |     | | | |   | | |     | | | | | | | |   | | |   |   | | |     | | | |   | | |     | | | | | | | |   | | |   |   | | +--+--+ | | |   | | +-----+ | | | | | | |   | | |   |   | | |  |  | | | +---+ | |     | | | | | | | +---+ | +---+---+ | |  |  | | | |   | | |_____| | | | | | | |   | | |   |   | | |  |  | | | |   | | |     | | | | | | | |   | | |   |   | | |  |  | | | |   | | |     | | | | | | | |   | | |   |   | +-+--+--+ +-+-+---+ +-+-----+ +-+-+-+-+ +-+---+-+ +---+---+ CROSSREFS Cf. A189243, A219861. Sequence in context: A150074 A349367 A300335 * A052863 A037128 A150075 Adjacent sequences:  A108063 A108064 A108065 * A108067 A108068 A108069 KEYWORD hard,more,nonn,nice AUTHOR Hans Riesebos (hans.riesebos(AT)wanadoo.nl) and Herman Beeksma, Jun 03 2005 STATUS approved

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