OFFSET
1,1
COMMENTS
log(u/v), where u = n + 1/2 and v = n - 1/2, is the area under the curve y = 1/x that matches the rectangle of width 1 and height 1/n with base centered at (1/n,0); a(n) -> oo since -1/n + log(u/v) -> 0.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = 12*n^3 - round(9*n/5) (conjectured, based on computations by Peter J. C. Moses, Jul 14 2013).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) + 3*a(n-7) - a(n-8) (conjectured; verified up to n = 100000 ).
G.f.: x*(10 + 62*x + 73*x^2 + 70*x^3 + 73*x^4 + 62*x^5 + 10*x^6)/((-1 + x)^4*(1 + x + x^2 + x^3 + x^4)) (conjectured).
EXAMPLE
-1/4 + log(9/7) = 0.0013144..., so 1/u = 760.78...,so a(4) = 761.
MATHEMATICA
z = 120; a[n_] := Round[1/(Log[(2 n + 1)/(2 n - 1)] - 1/n)]
t = Table[a[n], {n, 1, z}] (* A227513 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 14 2013
STATUS
approved