login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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: A101472 A273872 A087160 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 17 16:43 EST 2019. Contains 319235 sequences. (Running on oeis4.)