Search: id:A007569
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%I A007569 M0724
%S A007569 1,2,3,5,10,19,42,57,135,171,341,313,728,771,1380,1393,2397,1855,
%T A007569 3895,3861,6006,5963,8878,7321,12675,12507,17577,17277,23780,
%U A007569 16831,31496,30945,40953,40291,52395,47017,66082,65019,82290
%N A007569 Number of nodes in regular n-gon with all diagonals drawn.
%D A007569 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007569 T. D. Noe, <a href="b007569.txt">Table of n, a(n) for n=1..1000</a>
%H A007569 Sascha Kurz, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/drawing/
               drawing.html">m-gons in regular n-gons</a>
%H A007569 B. Poonen and M. Rubinstein, <a href="http://epubs.siam.org:80/sam-bin/
               dbq/article/28124">Number of Intersection Points Made by the Diagonals 
               of a Regular Polygon</a>, SIAM J. Discrete Mathematics, Vol. 11, 
               pp. 135-156.
%H A007569 B. Poonen and M. Rubinstein, <a href="http://math.mit.edu/~poonen/">The 
               number of intersection points made by the diagonals of a regular 
               polygon</a>, SIAM J. on Discrete Mathematics, Vol. 11, No. 1, 135-156 
               (1998).
%H A007569 B. Poonen and M. Rubinstein, <a href="http://arXiv.org/pdf/math.MG/9508209">
               The number of intersection points made by the diagonals of a regular 
               polygon</a>, arXiv version, which has fewer typos than the SIAM version.
%H A007569 B. Poonen and M. Rubinstein, <a href="http://math.mit.edu/~poonen/papers/
               ngon.m">Mathematica programs for these sequences</a>
%H A007569 <a href="Sindx_Pol.html#Poonen">Sequences formed by drawing all diagonals 
               in regular polygon</a>
%F A007569 a(n)=A006561(n)+n. - T. D. Noe, Dec 23 2006
%t A007569 del[m_,n_]:=If[Mod[n,m]==0,1,0]; Int[n_]:=If[n<4, n, n + Binomial[n,4] 
               + del[2,n](-5n^3+45n^2-70n+24)/24 - del[4,n](3n/2) + del[6,n](-45n^2+262n)/
               6 + del[12,n]*42n + del[18,n]*60n + del[24,n]*35n - del[30,n]*38n 
               - del[42,n]*82n - del[60,n]*330n - del[84,n]*144n - del[90,n]*96n 
               - del[120,n]*144n - del[210,n]*96n]; Table[Int[n], {n,1,1000}] - 
               T. D. Noe (noe(AT)sspectra.com), Dec 21 2006
%Y A007569 Sequences related to chords in a circle: A001006, A054726, A006533, A006561, 
               A006600, A007569, A007678. See also entries for chord diagrams in 
               Index file.
%Y A007569 Sequence in context: A166874 A046630 A064236 this_sequence A054317 A065840 
               A093785
%Y A007569 Adjacent sequences: A007566 A007567 A007568 this_sequence A007570 A007571 
               A007572
%K A007569 easy,nonn,nice
%O A007569 1,2
%A A007569 N. J. A. Sloane (njas(AT)research.att.com), Bjorn Poonen (poonen(AT)math.princeton.edu)

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