cp's OEIS Frontend

A244096 Rounded down area ratio of a circle inscribed in a congruent triangle of a regular n-gon and a circle inscribed between a side of such an n-gon and a circumscribed unit circle.

%I A244096 #25 Jun 13 2021 03:24:48
%S A244096 0,4,9,18,30,45,63,84,108,135,166,200,237,277,321,367,417,471,527,587,
%T A244096 649,716,785,858,933,1012,1095,1180,1269,1361,1456,1555,1656,1761,
%U A244096 1870,1981,2096,2214,2335,2459,2587,2718,2852,2989,3130,3274,3421,3571,3725,3881,4042
%N A244096 Rounded down area ratio of a circle inscribed in a congruent triangle of a regular n-gon and a circle inscribed between a side of such an n-gon and a circumscribed unit circle.
%H A244096 Kival Ngaokrajang, <a href="/A244096/a244096_3.pdf">Illustration of initial terms</a>
%F A244096 a(n) = floor((r1(n)/r2(n))^2) where r1(n) = (s(n)/2)*sqrt((2 - s(n))/(2 + s(n))) and r2(n) = (2 - c(n))/4 with s(n) = 2*sin(Pi/n), the side length (length unit 1), and c(n) = 2*cos(Pi/n), the length ratio of the smallest diagonal and the side of a regular n-gon. [Rewritten by _Wolfdieter Lang_, Jul 02 2014]
%o A244096 (PARI)
%o A244096 {
%o A244096   for (n=3, 100,
%o A244096      c=2*sin(Pi/n);
%o A244096      s=(2+c)/2;
%o A244096      r1=(((s-1)^2*(s-c))/s)^(1/2);
%o A244096      b=Pi*(n-2)/(2*n);
%o A244096      r2=(1-sin(b))/2;
%o A244096      a=floor(r1^2/r2^2);
%o A244096      print1(a,", ")
%o A244096   )
%o A244096 }
%Y A244096 Cf. A244093, A244094.
%K A244096 nonn
%O A244096 3,2
%A A244096 _Kival Ngaokrajang_, Jun 20 2014