an interesting new sequence!

[N. J. A. Sloane]

David was commenting on the old version of that sequence.

I revised it today.  Here is the current version.

NJAS

%I A107427
%S A107427 0,0,1,2,4,7,10,14,18,22
%N A107427 Maximal number of simple triangular regions that can be formed by drawing n line segments in the Euclidean plane.
%C A107427 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.
%C A107427 Inspection of Loy's web page shows that these are known to be optimal only for n up to about 7.
%C A107427 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
%H A107427 David Coles, <a href="http://davcoles.tripod.com">Triangle Puzzle</a>.
%H A107427 Jim Loy, <a href="http://www.jimloy.com/puzz/cole.htm">Triangle Puzzle</a>.
%H A107427 Jim Loy, <a href="http://www.research.att.com/~njas/sequences/a107427.gif">Illustration of a(6) = 7</a>
%e A107427 7 lines can make at most 10 triangles, so a(7) = 10.
%Y A107427 Cf. A000124.
%K A107427 nonn,nice,new,more
%O A107427 1,4
%A A107427 Bill Blewett (billble(AT)comcast.net), May 22 2005
%E A107427 Entry revised by njas, May 29 2005