Search: id:A006533
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%I A006533 M1118
%S A006533 1,2,4,8,16,30,57,88,163,230,386,456,794,966,1471,1712,2517,2484,
%T A006533 4048,4520,6196,6842,9109,9048,12951,14014,17902,19208,24158,
%U A006533 21510,31931,33888
%N A006533 Join n equal points around circle in all ways, count regions.
%D A006533 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006533 Jean Meeus, Wiskunde Post (Belgium), Vol. 10, 1972, pp. 62-63.
%H A006533 T. D. Noe, <a href="b006533.txt">Table of n, a(n) for n=1..1000</a>
%H A006533 Sascha Kurz, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/drawing/
               drawing.html">m-gons in regular n-gons</a>
%H A006533 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 A006533 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 A006533 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 A006533 B. Poonen and M. Rubinstein, <a href="http://math.mit.edu/~poonen/papers/
               ngon.m">Mathematica programs for these sequences</a>
%H A006533 <a href="Sindx_Pol.html#Poonen">Sequences formed by drawing all diagonals 
               in regular polygon</a>
%F A006533 a(n)=A007678(n)+n. - T. D. Noe, Dec 23 2006
%t A006533 del[m_,n_]:=If[Mod[n,m]==0,1,0]; R[n_]:=(n^4-6n^3+23n^2-18n+24)/24 + 
               del[2,n](-5n^3+42n^2-40n-48)/48 - del[4,n](3n/4) + del[6,n](-53n^2+310n)/
               12 + del[12,n](49n/2) + del[18,n]*32n + del[24,n]*19n - del[30,n]*36n 
               - del[42,n]*50n - del[60,n]*190n - del[84,n]*78n - del[90,n]*48n 
               - del[120,n]*78n - del[210,n]*48n; Table[R[n], {n,1,1000}] - T. D. 
               Noe (noe(AT)sspectra.com), Dec 21 2006
%Y A006533 Sequences related to chords in a circle: A001006, A054726, A006533, A006561, 
               A006600, A007569, A007678. See also entries for chord diagrams in 
               Index file.
%Y A006533 Sequence in context: A164256 A164240 A164214 this_sequence A164188 A164186 
               A164187
%Y A006533 Adjacent sequences: A006530 A006531 A006532 this_sequence A006534 A006535 
               A006536
%K A006533 nonn,easy,nice
%O A006533 1,2
%A A006533 N. J. A. Sloane (njas(AT)research.att.com), Bjorn Poonen (poonen(AT)math.princeton.edu)

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