%I #21 Nov 03 2024 04:33:40
%S 1,6,40,152,413,920,1792,3173,5232,8160,12173,17512,24440,33245,44240,
%T 57760,74165,93840,117192,144653,176680,213752,256373,305072,360400,
%U 422933,493272,572040,659885,757480,865520,984725,1115840,1259632,1416893,1588440,1775112
%N a(n) = floor(M(g(n-1)+1,..,g(n))), where M is the harmonic mean and g(n) = n^4.
%C See A227012.
%F a(n) = 47/9 + 14*n + (41*n^2)/3 + 6*n^3 + n^4 - (2/9)Cos(2*n*pi/3) (conjectured).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 5*a(n-3) - 5*a(n-4) + 6*a(n-5) - 4*a(n-6) + a(n-7) for n > 2 (conjectured).
%F G.f.: (-1 - 2*x - 22*x^2 - 23*x^3 - 20*x^4 - 4*x^5 + 2*x^6 - 3*x^7 + x^8)/((-1 + x)^5 (1 + x + x^2)) (conjectured).
%e a(1) = floor(1/(1/1)) = 1.
%e a(2) = floor(15/(1/2 + 1/3 + ... + 1/16)) = 6.
%t z = 30; f[x_] := f[x] = 1/x; g[n_] := g[n] = n^4; 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[Floor[v[n]], {n, 1, z}]
%Y Cf. A227012.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jul 01 2013
%E Extended by _Ray Chandler_, Jul 15 2015