OFFSET
1,2
COMMENTS
Also a(n) = floor(G(g(n-1)+1,g(n))), where G = geometric mean. See A227012.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
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)
EXAMPLE
a(1) = floor(1/(1/1)); a(2) = floor(4/(1/2 + 1/3 + 1/4 + 1/5)) = 3.
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}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 01 2013
STATUS
approved