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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005732 C(n+3,6)+C(n+1,5)+C(n,5).
(Formerly M4514)
2
1, 8, 35, 111, 287, 644, 1302, 2430, 4257, 7084, 11297, 17381, 25935, 37688, 53516, 74460, 101745, 136800, 181279, 237083, 306383, 391644, 495650, 621530, 772785, 953316, 1167453, 1419985, 1716191, 2061872, 2463384, 2927672, 3462305, 4075512, 4776219, 5574087, 6479551 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

COMMENTS

Place n points in general position on a circle, join them in all possible ways; how many triangles can be seen?

Equals binomial transform of [1, 7, 20, 29, 22, 8, 1, 0, 0, 0,...]. - Gary W. Adamson, Jun 13 2008

REFERENCES

R. J. Cormier and R. B. Eggleton, Counting by correspondence, Math. Mag., 49 (1976), 181-186.

C. L. Liu, Introduction to Combinatorial Analysis. McGraw-Hill, NY, 1968, p. 20.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n=3..1000

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

T. Sillke, Number of triangles for a convex n-gon

MAPLE

A005732:=(-1-z+z**3)/(z-1)**7; [Conjectured by Simon Plouffe in his 1992 dissertation.]

MATHEMATICA

Table[Binomial[n+3, 6]+Binomial[n+1, 5]+Binomial[n, 5], {n, 3, 40}]  (* Harvey P. Dale, Apr 09 2011 *)

PROG

(MAGMA) [Binomial(n+3, 6) + Binomial(n+1, 5) +Binomial(n, 5): n in [3..100]]; // Vincenzo Librandi, Apr 10 2011

(Haskell)

a005732 n = a005732_list !! (n-3)

a005732_list = 1 : 8 : f (drop 5 a007318_tabl) where

   f (us:pss@(vs:_:ws:_)) = (us !! 5 + vs !! 5 + ws !! 6) : f pss

-- Reinhard Zumkeller, Mar 11 2014

CROSSREFS

Often confused with A006600.

Cf. A007318.

Sequence in context: A244882 A006600 A161456 * A162211 A161717 A162494

Adjacent sequences:  A005729 A005730 A005731 * A005733 A005734 A005735

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Thanks to Joshua Zucker, Ted Alper and Joe Keane for clarifying the connection with A006600.

More terms from Harvey P. Dale, Apr 09 2011.

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified October 24 23:00 EDT 2014. Contains 248516 sequences.