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

0,2

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, Dodecahedron

Eric Weisstein's World of Mathematics, Platonic Solid

Formula

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

Example

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

Mathematica

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

Prog

(PARI) for(n=0, 100, print1(round(3*n^2*sqrt(25+10*sqrt(5))), ", "))
(Magma) [Round(3 * n^2 * Sqrt(25+10*Sqrt(5))): n in [0..50]]; // Vincenzo Librandi, May 21 2011

Crossrefs

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

Sequence in context: A195961 A359024 A190023 * A064762 A104676 A143244

Adjacent sequences: A071394 A071395 A071396 * A071398 A071399 A071400

Keyword

easy,nonn

Author

Rick L. Shepherd, May 28 2002

Status

approved