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

Author

Bill Blewett, May 22 2005

Keywords

• nonn
• nice
• more

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

Examples

			7 lines can make at most 10 triangles, so a(7) = 10.
		

Links

• David Coles, Triangle Puzzle.
• Jim Loy, Triangle Puzzle.
• Jim Loy, Illustration of a(6) = 7

Crossrefs

Cf. A000124.

Extensions

Entry revised by N. J. A. Sloane, May 29 2005