%I #11 Mar 11 2024 11:42:22

%S 0,0,1,1,2,3,4,6,7,9,11,13,15,17,20,22,25,28,31,34,38,41,45,49,53,57,

%T 62,66,71,76,81,86,91,97,102,108,114,120,127,133,140,146,153,160,168,

%U 175,183,190,198,206,214,223,231,240,249,258,267,276,286,295,305,315

%N Integer part of area of a regular polygon with n sides each of length 1.

%C Usually (perhaps always?) floor(n^2/(4*Pi) - Pi/12) for a polygon of circumference n. Note that the area of a circle with circumference C is C^2/(4*Pi).

%H Harry J. Smith, <a href="/A064313/b064313.txt">Table of n, a(n) for n = 2..1000</a>

%F a(n) = floor(n/(4*tan(Pi/n))).

%e Areas (starting from n=2) are: 0, 0.433... (equilateral triangle), 1 (square), 1.720... (pentagon), 2.598... (hexagon), 3.633... (heptagon), 4.828... (octagon), etc., so sequence starts 0, 0, 1, 1, 2, 3, 4, etc.

%p A064313 := proc(n) RETURN(floor((n/4)*cot(Pi/n))) end:

%t Table[ Floor[(n/4)*Cot[Pi/n]], {n, 2, 75} ]

%o (PARI) { for (n=2, 1000, if (n>2, a=n\(4*tan(Pi/n)), a=0); write("b064313.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 11 2009

%Y Cf. A134030.

%K nonn

%O 2,5

%A _Henry Bottomley_, Oct 15 2001