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 A107427 Maximal number of simple triangular regions that can be formed by drawing n line segments in the Euclidean plane. 1
 0, 0, 1, 2, 4, 7, 10, 14, 18, 22 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Draw n line segments on a piece of paper in such a way that if we make cuts along those lines, only triangular pieces are formed (apart from the "outside" region). Sequence gives maximal number of triangles that can be obtained. Inspection of Loy's web page shows that these are known to be optimal only for n up to about 7. Loy gives the following lower bounds for n = 1, 2, 3, ...: 0, 0, 1, 2, 4, 7, 10, 14, 18, 22, 27, 32, 38, 44, 50, 54, 60, 72, 76, 84, 92, 110, 114, 122, 130, 156, 160, 210 LINKS David Coles, Triangle Puzzle. Jim Loy, Triangle Puzzle. Jim Loy, Illustration of a(6) = 7 EXAMPLE 7 lines can make at most 10 triangles, so a(7) = 10. CROSSREFS Cf. A000124. Sequence in context: A101472 A273872 A087160 * A130251 A276208 A225635 Adjacent sequences:  A107424 A107425 A107426 * A107428 A107429 A107430 KEYWORD nonn,nice,more AUTHOR Bill Blewett, May 22 2005 EXTENSIONS Entry revised by N. J. A. Sloane, May 29 2005 STATUS approved

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Last modified January 17 16:43 EST 2019. Contains 319235 sequences. (Running on oeis4.)