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A244096
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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.
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3
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0, 4, 9, 18, 30, 45, 63, 84, 108, 135, 166, 200, 237, 277, 321, 367, 417, 471, 527, 587, 649, 716, 785, 858, 933, 1012, 1095, 1180, 1269, 1361, 1456, 1555, 1656, 1761, 1870, 1981, 2096, 2214, 2335, 2459, 2587, 2718, 2852, 2989, 3130, 3274, 3421, 3571, 3725, 3881, 4042
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OFFSET
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3,2
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LINKS
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FORMULA
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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]
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PROG
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(PARI)
{
for (n=3, 100,
c=2*sin(Pi/n);
s=(2+c)/2;
r1=(((s-1)^2*(s-c))/s)^(1/2);
b=Pi*(n-2)/(2*n);
r2=(1-sin(b))/2;
a=floor(r1^2/r2^2);
print1(a, ", ")
)
}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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