A071398 - OEIS

%I #16 Sep 08 2022 08:45:06

%S 0,9,35,78,139,217,312,424,554,701,866,1048,1247,1464,1697,1949,2217,

%T 2503,2806,3126,3464,3819,4192,4581,4988,5413,5854,6313,6790,7283,

%U 7794,8323,8868,9431,10011,10609,11224,11856,12505,13172,13856,14558,15277

%N Rounded total surface area of a regular icosahedron with edge length n.

%D S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, pp. 10-11.

%H Vincenzo Librandi, <a href="/A071398/b071398.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Icosahedron.html">Icosahedron</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PlatonicSolid.html">Platonic Solid</a>

%F a(n) = round(5 * n^2 * sqrt(3)).

%e a(4)=139 because round(5*4^2*sqrt(3)) = round(80*1.73205...) = round(138.56...) = 139.

%t With[{c=5Sqrt[3]},Round[c Range[0,50]^2]] (* _Harvey P. Dale_, May 20 2011 *)

%o (PARI) for(n=0,100,print1(round(5*n^2*sqrt(3)),","))

%o (Magma) [Round(5 * n^2 * Sqrt(3)): n in [0..50]]; // _Vincenzo Librandi_, May 21 2011

%Y Cf. A070169 (tetrahedron), A033581 (cube), A071396 (octahedron), A071397 (dodecahedron), A071402 (volume of icosahedron).

%K easy,nonn

%O 0,2

%A _Rick L. Shepherd_, May 29 2002