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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 01 2013
STATUS
approved