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A071397 Rounded total surface area of a regular dodecahedron with edge length n. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A219593 A195961 A190023 * A064762 A104676 A143244

Adjacent sequences:  A071394 A071395 A071396 * A071398 A071399 A071400

KEYWORD

easy,nonn

AUTHOR

Rick L. Shepherd, May 28 2002

STATUS

approved

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Last modified March 21 10:00 EDT 2019. Contains 321368 sequences. (Running on oeis4.)