OFFSET
1,1
COMMENTS
Numerators are b(n)=(-1)^(n+1) if n==0 (mod 3) b(n)=(-1)^(n+1)*3 otherwise.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).
FORMULA
a(n) = 2*n/3 if n==0 (mod 3), a(n) = 2*n, otherwise.
3*log(sqrt(1+x)) = (3/2)*log(1+x) = -3 * Sum_{k>=1} (-x)^k/(2*k).
MATHEMATICA
a[n_] := If[Mod[n, 3] == 0, 2*n/3, 2*n]; Array[a, 100] (* G. C. Greubel, Sep 21 2018 *)
PROG
(PARI) for(n=1, 100, print1(if(Mod(n, 3)==0, 2*n/3, 2*n), ", ")) \\ G. C. Greubel, Sep 21 2018
CROSSREFS
KEYWORD
easy,frac,nonn
AUTHOR
Benoit Cloitre, Mar 30 2002
EXTENSIONS
Log expression corrected by Kevin Ryde, Nov 01 2021
STATUS
approved