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A227017 Floor(M(g(n-1)+1,..,g(n))), where M = harmonic mean and g(n) = n(3n-1)/2 = A000326(n).

%I A227017 #20 Mar 17 2021 10:35:25
%S A227017 1,3,8,17,28,43,60,81,104,131,160,193,228,267,308,353,400,451,504,561,
%T A227017 620,683,748,817,888,963,1040,1121,1204,1291,1380,1473,1568,1667,1768,
%U A227017 1873,1980,2091,2204,2321,2440,2563,2688,2817,2948,3083,3220,3361,3504
%N A227017 Floor(M(g(n-1)+1,..,g(n))), where M = harmonic mean and g(n) = n(3n-1)/2 = A000326(n).
%C A227017 Also a(n) = floor(G(g(n-1)+1,g(n))), where G = geometric mean.  See A227012.
%H A227017 Clark Kimberling, <a href="/A227017/b227017.txt">Table of n, a(n) for n = 1..1000</a>
%F A227017 a(n) = (1/4)*(1 - (-1)^n + 4*n + 6*n^2) (conjectured).
%F A227017 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n > 1 (conjectured).
%F A227017 G.f.: (-1 - x - 2*x^2 - 3*x^3 + x^4)/((-1 + x)^3 (1 + x)). (conjectured)
%e A227017 a(1) = floor(1/(1/1)); a(2) = floor(4/(1/2 + 1/3 + 1/4 + 1/5)) = 3.
%t A227017 z = 100; f[x_] := f[x] = 1/x; g[n_] := g[n] = n (3 n - 1)/2; s[n_] := s[n] = Sum[f[k], {k, g[n - 1] + 1, g[n]}]; v[n_] := v[n] = (g[n] - g[n - 1])/s[n]; Table[g[n], {n, 1, z}]; Table[Floor[v[n]], {n, 1, z}]
%Y A227017 Cf. A227012.
%K A227017 nonn,easy
%O A227017 1,2
%A A227017 _Clark Kimberling_, Jul 01 2013