A244094 Rounded down ratio of area of a unit circle and one of the circles inscribed between a regular n-gon and a circumscribed unit circle.

16, 46, 109, 222, 407, 690, 1099, 1669, 2437, 3445, 4737, 6363, 8376, 10834, 13797, 17330, 21503, 26389, 32064, 38608, 46108, 54651, 64331, 75243, 87489, 101172, 116402, 133290, 151953, 172511, 195088, 219813, 246817, 276236, 308211, 342885, 380407, 420927, 464601, 511590

Offset: 3

Author

Kival Ngaokrajang, Jun 20 2014

Keywords

• nonn
• easy

Links

• Kival Ngaokrajang, Illustration of initial terms

Crossrefs

Cf. A244093, A244096.

Programs

PARI

{
  for (n=3, 100,
     b=Pi*(n-2)/(2*n);
     r=(1-sin(b))/2;
     area=Pi*r^2;
     a=floor(Pi/area);
     print1(a,", ")
  )
}

Formula

a(n) = floor(Pi/area(n)) where area(n) = Pi*r(n)^2, r(n) = (1 - cos(Pi/n))/2 = sin(Pi/(2*n))^2, n >= 3.

Extensions

Edited. Formula simplified - Wolfdieter Lang, Jun 27 2014