A171972 Greatest integer k such that k/n^2 < sqrt(3).

0, 1, 6, 15, 27, 43, 62, 84, 110, 140, 173, 209, 249, 292, 339, 389, 443, 500, 561, 625, 692, 763, 838, 916, 997, 1082, 1170, 1262, 1357, 1456, 1558, 1664, 1773, 1886, 2002, 2121, 2244, 2371, 2501, 2634, 2771, 2911, 3055, 3202, 3353, 3507, 3665, 3826, 3990, 4158

Offset: 0

Author

Reinhard Zumkeller, Jan 20 2010

Keywords

• nonn

Comments

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

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

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Tetrahedron
• Wikipedia, Tetrahedron

Crossrefs

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

Programs

Haskell

a171972 = floor . (* sqrt 3) . fromInteger . a000290
-- Reinhard Zumkeller, Dec 15 2012

Mathematica

z = 120; r = Sqrt[3];
Table[Floor[r*n^2], {n, 0, z}]; (* A171972 *)
Table[Ceiling[r*n^2], {n, 0, z}]; (* A293410 *)
Table[Round[r*n^2], {n, 0, z}]; (* A070169. -  Clark Kimberling, Oct 11 2017 *)

Formula

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

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

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