A071398 Rounded total surface area of a regular icosahedron with edge length n.

0, 9, 35, 78, 139, 217, 312, 424, 554, 701, 866, 1048, 1247, 1464, 1697, 1949, 2217, 2503, 2806, 3126, 3464, 3819, 4192, 4581, 4988, 5413, 5854, 6313, 6790, 7283, 7794, 8323, 8868, 9431, 10011, 10609, 11224, 11856, 12505, 13172, 13856, 14558, 15277

Offset

0,2

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Icosahedron

Eric Weisstein's World of Mathematics, Platonic Solid

Formula

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

Example

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

Mathematica

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

Prog

(PARI) for(n=0, 100, print1(round(5*n^2*sqrt(3)), ", "))
(Magma) [Round(5 * n^2 * Sqrt(3)): n in [0..50]]; // Vincenzo Librandi, May 21 2011

Crossrefs

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

Sequence in context: A033566 A226755 A022275 * A212099 A212100 A005898

Adjacent sequences: A071395 A071396 A071397 * A071399 A071400 A071401

Keyword

easy,nonn

Author

Rick L. Shepherd, May 29 2002

Status

approved