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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.
EXAMPLE
7 lines can make at most 10 triangles, so a(7) = 10.
CROSSREFS
Cf. A000124.
Sequence in context: A273872 A087160 A336411 * A130251 A276208 A225635
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 March 29 03:41 EDT 2024. Contains 371264 sequences. (Running on oeis4.)