

A244096


Rounded down area ratio of a circle inscribed in a congruent triangle of a regular ngon and a circle inscribed between side of such ngon and a circumscribed unit circle.


3



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

3,2


LINKS

Table of n, a(n) for n=3..53.
Kival Ngaokrajang, Illustration of initial terms


FORMULA

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 ngon.


PROG

(PARI)
{
for (n=3, 100,
c=2*sin(Pi/n);
s=(2+c)/2;
r1=(((s1)^2*(sc))/s)^(1/2);
b=Pi*(n2)/(2*n);
r2=(1sin(b))/2;
a=floor(r1^2/r2^2);
print1(a, ", ")
)
}


CROSSREFS

Cf. A244093, A244094.
Sequence in context: A008025 A301196 A008020 * A008146 A038098 A299274
Adjacent sequences: A244093 A244094 A244095 * A244097 A244098 A244099


KEYWORD

nonn


AUTHOR

Kival Ngaokrajang, Jun 20 2014


EXTENSIONS

Edited: Formula rewritten.  Wolfdieter Lang, Jul 02 2014


STATUS

approved



