cp's OEIS Frontend

A227015 a(n) = floor(M(g(n-1)+1, ..., g(n))), where M = harmonic mean and g(n) = n^3 + n^2 + n + 1.

%I A227015 #29 Mar 17 2021 13:07:21
%S A227015 2,8,26,60,117,203,324,487,696,958,1279,1666,2123,2657,3274,3981,4782,
%T A227015 5684,6693,7816,9057,10423,11920,13555,15332,17258,19339,21582,23991,
%U A227015 26573,29334,32281,35418,38752,42289,46036,49997,54179,58588,63231,68112,73238
%N A227015 a(n) = floor(M(g(n-1)+1, ..., g(n))), where M = harmonic mean and g(n) = n^3 + n^2 + n + 1.
%C A227015 See A227012.
%H A227015 Clark Kimberling, <a href="/A227015/b227015.txt">Table of n, a(n) for n = 1..100</a>
%F A227015 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 3*a(n-5) + 3*a(n-6) - a(n-7) for n > 2 (conjectured).
%F A227015 G.f.: x*(2 + 2*x + 8*x^2 + 4*x^3 + 5*x^4 + 4*x^5 - 2*x^6 + 3*x^7 - 3*x^8 + x^9)/((x - 1)^4*(1 + x + x^2 + x^3)) (conjectured).
%F A227015 From _Franck Maminirina Ramaharo_, Apr 16 2018: (Start)
%F A227015 a(n) = (1/2)*((-1)^(n - 1)! + 2*n^3 - n^2 + n + 3 + 2*floor(max(0, n - 4)/4)) (conjectured).
%F A227015 E.g.f.: (1/24)*exp(-x)*(exp(x)*(6*sin(x) + 6*cos(x) + 4*x^3 - 24) + exp(2*x)*(24*x^3 + 60*x^2 + 30*x + 15) + 3) (conjectured).
%F A227015 (End)
%t A227015 z = 100; f[x_] := f[x] = 1/x; g[n_] := g[n] = n^3 + n^2 + n + 1; 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}];
%t A227015 Table[Floor[v[n]], {n, 1, z}]
%Y A227015 Cf. A227012, A227013.
%K A227015 nonn
%O A227015 1,1
%A A227015 _Clark Kimberling_, Jul 01 2013