A255605 Integer part of the area of a pentagon with side length n.

1, 6, 15, 27, 43, 61, 84, 110, 139, 172, 208, 247, 290, 337, 387, 440, 497, 557, 621, 688, 758, 832, 910, 990, 1075, 1163, 1254, 1348, 1446, 1548, 1653, 1761, 1873, 1988, 2107, 2229, 2355, 2484, 2616, 2752, 2892, 3034, 3181, 3330, 3483, 3640, 3800, 3963, 4130, 4301, 4474

Offset: 1

Author

Kival Ngaokrajang, Feb 27 2015

Keywords

• nonn

Comments

Column 3 of A255604.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A102771, A255604.

Programs

Mathematica

Table[IntegerPart[5*n^2/(4*Tan[Pi/5])], {n, 51}] (* Michael De Vlieger, Mar 18 2015 *)
With[{c=Sqrt[25+10*Sqrt[5]]/4},Table[IntegerPart[c*n^2],{n,60}]] (* Harvey P. Dale, Aug 17 2020 *)

PARI

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

PARI

my(c=25+10*quadgen(20)); a(n) = sqrtint(floor(c*n^4))>>2; \\ Kevin Ryde, May 07 2021

Formula

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