A071397 Rounded total surface area of a regular dodecahedron with edge length n.

0, 21, 83, 186, 330, 516, 743, 1012, 1321, 1672, 2065, 2498, 2973, 3489, 4047, 4645, 5285, 5967, 6689, 7453, 8258, 9105, 9993, 10922, 11892, 12904, 13957, 15051, 16186, 17363, 18581, 19841, 21141, 22483, 23866, 25291, 26757, 28264, 29812

Offset: 0

Author

Rick L. Shepherd, May 28 2002

Keywords

• easy
• nonn

Examples

			a(4)=330 because round(3*4^2*sqrt(25 + 10*sqrt(5))) = round(48*6.88190...) = round(330.331...) = 330.
		

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, Dodecahedron
• Eric Weisstein's World of Mathematics, Platonic Solid

Crossrefs

Cf. A070169 (tetrahedron), A033581 (cube), A071396 (octahedron), A071398 (icosahedron), A071401 (volume of dodecahedron).

Programs

Magma

[Round(3 * n^2 * Sqrt(25+10*Sqrt(5))): n in [0..50]]; // Vincenzo Librandi, May 21 2011

Mathematica

With[{c=3*Sqrt[25+10*Sqrt[5]]},Round[c*Range[0,40]^2]] (* Harvey P. Dale, Jul 06 2018 *)

PARI

for(n=0,100,print1(round(3*n^2*sqrt(25+10*sqrt(5))),","))

Formula

a(n) = round(3 * n^2 * sqrt(25 + 10*sqrt(5))).