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

3,1

Links

Table of n, a(n) for n=3..42.

Kival Ngaokrajang, Illustration of initial terms

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.

Prog

(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, ", ")
  )
}

Crossrefs

Cf. A244093, A244096.

Sequence in context: A069128 A099003 A124709 * A235549 A126370 A133345

Adjacent sequences: A244091 A244092 A244093 * A244095 A244096 A244097

Keyword

nonn,easy

Author

Kival Ngaokrajang, Jun 20 2014

Extensions

Edited. Formula simplified - Wolfdieter Lang, Jun 27 2014

Status

approved