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A244096 Rounded down area ratio of a circle inscribed in a congruent triangle of a regular n-gon and a circle inscribed between side of such n-gon 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 (list; graph; refs; listen; history; text; internal format)
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 n-gon.

PROG

(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, ", ")

  )

}

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

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Last modified November 26 01:22 EST 2020. Contains 338631 sequences. (Running on oeis4.)