cp's OEIS Frontend

A171974 Integer part of the height of a regular tetrahedron with edge length n.

%I A171974 #14 Feb 16 2025 08:33:11
%S A171974 0,1,2,3,4,4,5,6,7,8,8,9,10,11,12,13,13,14,15,16,17,17,18,19,20,21,22,
%T A171974 22,23,24,25,26,26,27,28,29,30,31,31,32,33,34,35,35,36,37,38,39,40,40,
%U A171974 41,42,43,44,44,45,46,47,48,48,49,50,51,52,53,53,54,55,56,57,57,58,59
%N A171974 Integer part of the height of a regular tetrahedron with edge length n.
%C A171974 -3 <= 4*A171975(n) - 3*a(n) < 3;
%C A171974 a(n)*A171975(n) <= A007590(n);
%C A171974 floor(a(n)*A171971(n)/3) <= A171973(n).
%H A171974 Reinhard Zumkeller, <a href="/A171974/b171974.txt">Table of n, a(n) for n = 1..1000</a>
%H A171974 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Tetrahedron.html">Tetrahedron</a>
%H A171974 Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetrahedron">Tetrahedron</a>
%H A171974 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F A171974 a(n) = floor(n*sqrt(6)/3).
%o A171974 (Haskell)
%o A171974 a171974 = floor . (/ 3) . (* sqrt 6) . fromInteger
%o A171974 -- _Reinhard Zumkeller_, Dec 15 2012
%Y A171974 Cf. A171972, A022840. Beatty sequence of A157697.
%Y A171974 Cf. A007590, A171971, A171973, A171975.
%K A171974 nonn
%O A171974 1,3
%A A171974 _Reinhard Zumkeller_, Jan 20 2010