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%I #36 Mar 23 2024 21:04:39
%S 0,0,6,7,24,36,90,132,168,234,378,600,672,901,954,1444,1580,2520,2860,
%T 2990,3696,4800,5070,6750,7644,9309,7920,12927,12896,15576,16898,
%U 20475,18684,25382,27246,30966,32760,37064,37170,45838,47300,55350,60996,69231,66864,80507,87550,98124,103272
%N Number of regions in regular n-gon which are quadrilaterals (4-gons) when all its diagonals are drawn.
%D B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.
%H Scott R. Shannon, <a href="/A067151/b067151.txt">Table of n, a(n) for n = 4..765</a>
%H Sascha Kurz, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/drawing/drawing.html">m-gons in regular n-gons</a>
%H B. Poonen and M. Rubinstein, <a href="https://arxiv.org/abs/math/9508209">The number of intersection points made by the diagonals of a regular polygon</a>, arXiv:math/9508209 [math.MG], 1995-2006, which has fewer typos than the SIAM version.
%H B. Poonen and M. Rubinstein, <a href="http://math.mit.edu/~poonen/papers/ngon.m">Mathematica programs for these sequences</a>
%H <a href="/index/Pol#Poonen">Sequences formed by drawing all diagonals in regular polygon</a>
%F Conjecture: a(n) ~ c * n^4. Is c = 1/64 ? - _Bill McEachen_, Mar 03 2024
%e a(6)=6 because the 6 regions around the center are quadrilaterals.
%Y Cf. A007678, A067163, A064869, A067152, A067153, A067154, A067155, A067156, A067157, A067158, A067159.
%K nonn
%O 4,3
%A _Sascha Kurz_, Jan 06 2002
%E Title clarified, a(47) and above by _Scott R. Shannon_, Dec 04 2021
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