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%I #16 Feb 22 2015 23:38:15
%S 1,2,-12,168,-2160,27936,-361152,4669056,-60362496,780378624,
%T -10088893440,130431264768,-1686241898496,21800077959168,
%U -281835838291968,3643630995013632,-47105601999667200,608990795936169984,-7873156775230046208
%N Irrational parts of circle radii in nested circles and hexagons (see comment).
%C Inspired by Vitruvian Man, but using hexagons instead of squares, starting with a hexagon whose sides are of length 4 (in some units). The radius of the circle is an integer in the real quadratic number field Q(sqrt(3)), namely R(n) = A(n) + B(n)*sqrt(3) with A(0)=2, A(n) = A255162(n), and B(0) = 1, B(n) = a(n). See illustrations in the links.
%H Kival Ngaokrajang, <a href="/A255163/a255163_2.pdf">Illustration of initial terms</a>, <a href="/A255163/a255163_1.pdf">Vitruvian Man</a>
%F Conjectures from _Colin Barker_, Feb 15 2015: (Start)
%F a(n) = -12*a(n-1) + 12*a(n-2).
%F G.f.: -(14*x+1) / (12*x^2-12*x-1).
%F (End)
%o (PARI){a=2;b=1;print1(b,", ");for(n=1,30,c=12*b-6*a;d=4*a-6*b;print1(d,", ");a=c;b=d)}
%Y Cf. A174968, A170931, A094013, A255162.
%K sign
%O 0,2
%A _Kival Ngaokrajang_, Feb 15 2015
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