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 A359146 Divide a square into n similar rectangles; a(n) is the number of different proportions that are possible. 2
 1, 1, 3, 11, 51, 245, 1372 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Only the proportions of the rectangles are counted, not how the rectangles are arranged in the square. The number b(n) of different ways to divide a square into n similar rectangles, up to rotation and reflection, is at least a(n). We have b(1)=1, b(2)=1, b(3)=3, and Baez remarks that b(4) > 11. It would be nice to know more. Is the sequence {b(n)} already in the OEIS? REFERENCES Siobhan Roberts, An Online Puzzle Excites Math Fans, New York Times, Feb 07 2023, pages D1 and D4. LINKS John Baez, Rahul Narain, Daniel Piker, Lisanne Taams, Ian Henderson, David Eppstein, and others, Dividing a Square into Similar Rectangles, First posted Dec. 22 2022, with many later comments John Baez, Dividing a Square into 7 Similar Rectangles, Mar 06 2023. Continuation of first blog entry, with a new value for a(7). Ian Henderson, Cutting squares into similar rectangles using a computer program, Feb 02 2023 Siobhan Roberts, The Quest to Find Rectangles in a Square, New York Times, Feb 07 2023 N. J. A. Sloane, Illustration for a(3) = 3 CROSSREFS Cf. A100664, A108066, A348456. Sequence in context: A145144 A284702 A191341 * A199212 A113283 A326519 Adjacent sequences: A359143 A359144 A359145 * A359147 A359148 A359149 KEYWORD nonn,more AUTHOR N. J. A. Sloane, Feb 07 2023 EXTENSIONS It appears that a(8) = 8522. - Ian Henderson, Feb 07, 2023, corrected Mar 07 2023 a(7) corrected by N. J. A. Sloane, Mar 07 2023, based on the second John Baez blog entry. STATUS approved

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Last modified March 25 19:21 EDT 2023. Contains 361528 sequences. (Running on oeis4.)