Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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