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URL: https://oeis.org/A171972

⇱ A171972 - OEIS

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A171972
Greatest integer k such that k/n^2 < sqrt(3).
8
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
0,3
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
Eric Weisstein's World of Mathematics, Tetrahedron
Wikipedia, Tetrahedron
FORMULA
a(n) = floor(n^2 * sqrt(3)).
a(n) = A022838(n^2);
a(n) = A293410(n) - 1 for n > 0.
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 *)
PROG
(Haskell)
a171972 = floor . (* sqrt 3) . fromInteger . a000290
-- Reinhard Zumkeller, Dec 15 2012
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jan 20 2010
STATUS
approved