login
A360792
Integer portion of area of inscribed circle in a regular polygon having n sides of unit length.
0
0, 0, 1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 17, 19, 22, 25, 28, 31, 34, 37, 41, 45, 49, 53, 57, 61, 66, 71, 75, 80, 86, 91, 96, 102, 108, 114, 120, 126, 133, 139, 146, 153, 160, 167, 175, 182, 190, 198, 206, 214, 223, 231, 240, 249, 258, 267, 276, 285, 295, 305
OFFSET
3,4
FORMULA
a(n) = floor((Pi/4)*(cot(Pi/n)^2)).
EXAMPLE
For n = 5, the circle inscribed in a regular pentagon with sides of unit length has area (Pi/4)*cot(Pi/5)^2 = 1.4878796365..., so a(5) = floor(1.4878796365...) = 1.
MAPLE
a:= n-> floor(Pi/(2*tan(Pi/n))^2):
seq(a(n), n=3..65); # Alois P. Heinz, Feb 20 2023
MATHEMATICA
a[n_] := Floor[(Pi/4)*Cot[Pi/n]^2]; Array[a, 60, 3] (* Amiram Eldar, Feb 24 2023 *)
PROG
(PARI) a(n) = floor((Pi/4)/tan(Pi/n)^2) \\ Andrew Howroyd, Feb 20 2023
CROSSREFS
Sequence in context: A375581 A320848 A228234 * A060526 A301599 A036408
KEYWORD
nonn
AUTHOR
A. Timothy Royappa, Feb 20 2023
EXTENSIONS
More terms from Andrew Howroyd, Feb 20 2023
STATUS
approved