login
Integer part of the area of a pentagon with side length n.
3

%I #18 May 07 2021 08:09:15

%S 1,6,15,27,43,61,84,110,139,172,208,247,290,337,387,440,497,557,621,

%T 688,758,832,910,990,1075,1163,1254,1348,1446,1548,1653,1761,1873,

%U 1988,2107,2229,2355,2484,2616,2752,2892,3034,3181,3330,3483,3640,3800,3963,4130,4301,4474

%N Integer part of the area of a pentagon with side length n.

%C Column 3 of A255604.

%H Harvey P. Dale, <a href="/A255605/b255605.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = floor(5*n^2/(4*tan(Pi/5))), n >= 1.

%t Table[IntegerPart[5*n^2/(4*Tan[Pi/5])], {n, 51}] (* _Michael De Vlieger_, Mar 18 2015 *)

%t With[{c=Sqrt[25+10*Sqrt[5]]/4},Table[IntegerPart[c*n^2],{n,60}]] (* _Harvey P. Dale_, Aug 17 2020 *)

%o (PARI){for(n=1,100,a=floor(5*n^2/(4*tan(Pi/5)));print1(a,", "))}

%o (PARI) my(c=25+10*quadgen(20)); a(n) = sqrtint(floor(c*n^4))>>2; \\ _Kevin Ryde_, May 07 2021

%Y Cf. A102771, A255604.

%K nonn

%O 1,2

%A _Kival Ngaokrajang_, Feb 27 2015