1,4

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

David Coles, Triangle Puzzle.

Jim Loy, Triangle Puzzle.

Jim Loy, Illustration of a(6) = 7

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

Cf. A000124.

Sequence in context: A049983 A101472 A087160 this_sequence A130251 A024611 A088236

Adjacent sequences: A107424 A107425 A107426 this_sequence A107428 A107429 A107430

nonn,nice,more

Bill Blewett (billble(AT)comcast.net), May 22 2005

Entry revised by njas, May 29 2005