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

1,2

Comments

Column 3 of A255604.

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A102771, A255604.

Sequence in context: A373384 A316320 A140091 * A171972 A225285 A353603

Adjacent sequences: A255602 A255603 A255604 * A255606 A255607 A255608

Keyword

nonn

Author

Kival Ngaokrajang, Feb 27 2015

Status

approved