The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A171972 Greatest integer k such that k/n^2 < sqrt(3). 8

%I

%S 0,1,6,15,27,43,62,84,110,140,173,209,249,292,339,389,443,500,561,625,

%T 692,763,838,916,997,1082,1170,1262,1357,1456,1558,1664,1773,1886,

%U 2002,2121,2244,2371,2501,2634,2771,2911,3055,3202,3353,3507,3665,3826,3990,4158

%N Greatest integer k such that k/n^2 < sqrt(3).

%C Integer part of the surface area of a regular tetrahedron with edge length n.

%C A171970(n)*A005843(n) <= a(n);

%C a(n) <= 4*A171971(n); 0 <= a(n) - 4*A171971(n) < 4.

%H Reinhard Zumkeller, <a href="/A171972/b171972.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Tetrahedron.html">Tetrahedron</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetrahedron">Tetrahedron</a>

%F a(n) = floor(n^2 * sqrt(3)).

%F a(n) = A022838(n^2);

%F a(n) = A293410(n) - 1 for n > 0.

%t z = 120; r = Sqrt[3];

%t Table[Floor[r*n^2], {n, 0, z}]; (* A171972 *)

%t Table[Ceiling[r*n^2], {n, 0, z}]; (* A293410 *)

%t Table[Round[r*n^2], {n, 0, z}]; (* A070169. - _Clark Kimberling_, Oct 11 2017 *)

%o a171972 = floor . (* sqrt 3) . fromInteger . a000290

%o -- _Reinhard Zumkeller_, Dec 15 2012

%Y Cf. A002194, A070169, A171974, A171973, A171975, A000290, A293410.

%K nonn

%O 0,3

%A _Reinhard Zumkeller_, Jan 20 2010

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 23 08:18 EDT 2020. Contains 337295 sequences. (Running on oeis4.)