A227013 a(n) = floor(M(g(n-1)+1,..,g(n))), where M is the harmonic mean and g(n) = n^4.

1, 6, 40, 152, 413, 920, 1792, 3173, 5232, 8160, 12173, 17512, 24440, 33245, 44240, 57760, 74165, 93840, 117192, 144653, 176680, 213752, 256373, 305072, 360400, 422933, 493272, 572040, 659885, 757480, 865520, 984725, 1115840, 1259632, 1416893, 1588440, 1775112

Offset

1,2

Comments

See A227012.

Links

Table of n, a(n) for n=1..37.

Formula

a(n) = 47/9 + 14*n + (41*n^2)/3 + 6*n^3 + n^4 - (2/9)Cos(2*n*pi/3) (conjectured).

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).

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).

Example

a(1) = floor(1/(1/1)) = 1, a(2) = floor(15/(1/2 + 1/3 + ... + 1/16) = 6.

Mathematica

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}]

Crossrefs

Cf. A227012.

Sequence in context: A089207 A318169 A027777 * A073773 A001919 A342404

Adjacent sequences: A227010 A227011 A227012 * A227014 A227015 A227016

Keyword

nonn,easy

Author

Clark Kimberling, Jul 01 2013

Extensions

Extended by Ray Chandler, Jul 15 2015

Status

approved