The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60, we have over 367,000 sequences, and we’ve crossed 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A108066 Number of distinct ways to dissect a square into n rectangles of equal area. 6
 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 David Wells, Penguin Dictionary of Curious and Interesting Geometry, 1991, pp. 15-16. LINKS Table of n, a(n) for n=1..10. Blanche Descartes, Divisions of a square into rectangles, Eureka, No. 34 (1971), 31-35. 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).. N. J. A. Sloane, Blanche Descartes's dissection into 7 pieces with equal areas but different shapes. 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, A359146. 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 21:21 EST 2023. Contains 367502 sequences. (Running on oeis4.)