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A070169 Rounded total surface area of a regular tetrahedron with edge length n. 9
0, 2, 7, 16, 28, 43, 62, 85, 111, 140, 173, 210, 249, 293, 339, 390, 443, 501, 561, 625, 693, 764, 838, 916, 998, 1083, 1171, 1263, 1358, 1457, 1559, 1665, 1774, 1886, 2002, 2122, 2245, 2371, 2501, 2634, 2771, 2912, 3055, 3203, 3353, 3507, 3665, 3826, 3991 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the integer k that minimizes |k/n^2 - sqrt(3)|.  - Clark Kimberling, Oct 11 2017

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, Tetrahedron

Eric Weisstein's World of Mathematics, Platonic Solid

FORMULA

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

a(n) = A000194(n^4 + 3). - Christian Krause, Aug 04 2021

EXAMPLE

a(3)=16 because round(3^2*sqrt(3)) = round(9*1.73205...) = round(15.5884...) = 16.

MATHEMATICA

Round[Sqrt[3]#]&/@(Range[0, 50]^2) (* Harvey P. Dale, Sep 24 2012 *)

PROG

(PARI) for(n=0, 100, print1(round(n^2*sqrt(3)), ", "))

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

CROSSREFS

Cf. A033581 (cube), A071396 (octahedron), A071397 (dodecahedron), A071398 (icosahedron), A071399 (volume of tetrahedron).

Sequence in context: A229595 A083508 A048231 * A293410 A348270 A162420

Adjacent sequences:  A070166 A070167 A070168 * A070170 A070171 A070172

KEYWORD

easy,nonn

AUTHOR

Rick L. Shepherd, Apr 24 2002

STATUS

approved

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Last modified December 1 05:33 EST 2021. Contains 349426 sequences. (Running on oeis4.)