A070169 Rounded total surface area of a regular tetrahedron with edge length n.

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

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(3*n^4). - Christian Krause, Aug 04 2021; corrected by Chai Wah Wu, Jun 19 2024

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
(Python)
from math import isqrt
def A070169(n): return (m:=isqrt(k:=3*n**4))+(k-m*(m+1)>=1) # Chai Wah Wu, Jun 19 2024

Crossrefs

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

Sequence in context: A083508 A048231 A357577 * A293410 A348270 A162420

Adjacent sequences: A070166 A070167 A070168 * A070170 A070171 A070172

Keyword

easy,nonn

Author

Rick L. Shepherd, Apr 24 2002

Status

approved