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 A165633 Number of tatami-free rooms of given size A165632(n). 7
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 4, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 4, 2, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,14 COMMENTS Number of rectangles of size A165632(n) which cannot be tiled with tatamis of size 1x2 such that not more than 3 tatamis meet at any point. LINKS Table of n, a(n) for n=1..105. Project Euler, Problem 256: Tatami-Free Rooms, Sept. 2009. FORMULA A165633 = #{ {r,c} | rc = A165632(n) }. EXAMPLE a(1)=1 because the rectangle of size 7x10 is the only one of size 70 that cannot be filled with 2x1 tiles without having 4 tiles meet in some point. a(237)=5 because there are 5 different rectangles of size A165632(237)=1320 which cannot be tiled in the given way. CROSSREFS Cf. A068920. Sequence in context: A043280 A030379 A030392 * A349236 A117456 A030621 Adjacent sequences: A165630 A165631 A165632 * A165634 A165635 A165636 KEYWORD nonn AUTHOR M. F. Hasler, Sep 26 2009 STATUS approved

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Last modified September 9 07:24 EDT 2024. Contains 375762 sequences. (Running on oeis4.)