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A071397
Rounded total surface area of a regular dodecahedron with edge length n.
5
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
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
KEYWORD
easy,nonn
AUTHOR
Rick L. Shepherd, May 28 2002
STATUS
approved