A107427 Maximal number of simple triangular regions that can be formed by drawing n line segments in the Euclidean plane.

0, 0, 1, 2, 4, 7, 10, 14, 18, 22

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

Table of n, a(n) for n=1..10.

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: A273872 A087160 A336411 * 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