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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 (list; graph; refs; listen; history; text; internal format)
 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 Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 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 CROSSREFS Cf. A002194, A070169, A171974, A171973, A171975, A000290, A293410. Sequence in context: A316320 A140091 A255605 * A225285 A165454 A063525 Adjacent sequences:  A171969 A171970 A171971 * A171973 A171974 A171975 KEYWORD nonn AUTHOR Reinhard Zumkeller, Jan 20 2010 STATUS approved

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Last modified October 14 05:08 EDT 2019. Contains 327995 sequences. (Running on oeis4.)