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

1, 3, 8, 17, 28, 43, 60, 81, 104, 131, 160, 193, 228, 267, 308, 353, 400, 451, 504, 561, 620, 683, 748, 817, 888, 963, 1040, 1121, 1204, 1291, 1380, 1473, 1568, 1667, 1768, 1873, 1980, 2091, 2204, 2321, 2440, 2563, 2688, 2817, 2948, 3083, 3220, 3361, 3504

Offset: 1

Author

Clark Kimberling, Jul 01 2013

Keywords

• nonn
• easy

Comments

Also a(n) = floor(G(g(n-1)+1,g(n))), where G = geometric mean. See A227012.

Examples

			a(1) = floor(1/(1/1)); a(2) = floor(4/(1/2 + 1/3 + 1/4 + 1/5)) = 3.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A227012.

Programs

Mathematica

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}]

Formula

a(n) = (1/4)*(1 - (-1)^n + 4*n + 6*n^2) (conjectured).

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n > 1 (conjectured).

G.f.: (-1 - x - 2*x^2 - 3*x^3 + x^4)/((-1 + x)^3 (1 + x)). (conjectured)