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

2, 8, 26, 60, 117, 203, 324, 487, 696, 958, 1279, 1666, 2123, 2657, 3274, 3981, 4782, 5684, 6693, 7816, 9057, 10423, 11920, 13555, 15332, 17258, 19339, 21582, 23991, 26573, 29334, 32281, 35418, 38752, 42289, 46036, 49997, 54179, 58588, 63231, 68112, 73238

Offset: 1

Author

Clark Kimberling, Jul 01 2013

Keywords

• nonn

Comments

See A227012.

Links

• Clark Kimberling, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A227012, A227013.

Programs

Mathematica

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}];
Table[Floor[v[n]], {n, 1, z}]

Formula

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).

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).

From Franck Maminirina Ramaharo, Apr 16 2018: (Start)

a(n) = (1/2)*((-1)^(n - 1)! + 2*n^3 - n^2 + n + 3 + 2*floor(max(0, n - 4)/4)) (conjectured).

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).

(End)