A227016 Floor(M(g(n-1)+1,..,g(n))), where M = harmonic mean and g(n) = n(n + 1)(n + 2)/6.

1, 2, 7, 14, 27, 45, 69, 101, 141, 191, 252, 323, 408, 506, 618, 746, 890, 1052, 1233, 1432, 1653, 1895, 2159, 2447, 2759, 3097, 3462, 3853, 4274, 4724, 5204, 5716, 6260, 6838, 7451, 8098, 8783, 9505, 10265, 11065, 11905, 12787, 13712, 14679, 15692, 16750

Offset

1,2

Comments

See A227012.

Links

Clark Kimberling, Table of n, a(n) for n = 1..200

Formula

a(n) + 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-8) - 3*a(n-9) + 3*a(n-10) - a(n-11) for n > 1 (conjectured).

G.f.: (1 - x + 4*x^2 - 2*x^3 + 4*x^4 - x^5 + x^6 + 2*x^7 - x^8 + 3*x^9 - 3*x^10 + x^11)/((x - 1)^4 (1+x) (1+x^2) (1+x^4)) (conjectured). (G.f. found by Peter J. C. Moses, Jul 01 2013)

Example

a(1) = floor(1/(1/1)) = 1; a(2) = floor(3/(1/2 + 1/3 + 1/4)) = 2; a(3) = floor(6/(1/5 + 1/6 + ... + 1/10)) = 7.

Mathematica

z = 200; f[x_] := f[x] = 1/x; g[n_] := g[n] = n (n + 1) (n + 2)/6; 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}]

Crossrefs

Cf. A227012, A227013.

Sequence in context: A367954 A333644 A014112 * A268347 A210728 A294533

Adjacent sequences: A227013 A227014 A227015 * A227017 A227018 A227019

Keyword

nonn,easy

Author

Clark Kimberling, Jul 01 2013

Status

approved