OFFSET
0,1
COMMENTS
This sequence gives a measure of the convergence rate of sum{1/C(h,[h/2]), h = 0..k}. It appears that a(n+1) - a(n) is in {2,3} for n >= 0.
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..1000
EXAMPLE
Let s(n) = sum{1/C(2h+1,h), h = 0..n}. Approximations are shown here:
n ... r - s(n) ... 1/2^n
0 ... 2.2092 ..... 1
1 ... 1.2092 ..... 0.5
2 ... 0.7092 ..... 0.25
3 ... 0.375866 ... 0.125
4 ... 0.2092 ..... 0.0625
5 ... 0.1092 ..... 0.0635
6 ... 0.05919 .... 0.0156
7 ... 0.03063 .... 0.007812
8 ... 0.01634 .... 0.003906
9 ... 0.00840 .... 0.001953
a(6) = 9 because r - s(9) < 1/64 < r - s(8).
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 04 2014
STATUS
approved