OFFSET
1,3
COMMENTS
It appears that the sequence is always in simplest terms when generated.
What happens when we generalize this to r(1) = r(2) = a/b?
FORMULA
r(n) = a(n)/A289910(n).
EXAMPLE
For n=3 r(3)=1/r(2) + r(1) which is 5/2 = 2/1 + 1/2.
For n=4 r(4)= 2/1 + 5/2 = 9/2.
For n=5 r(5)= 2/5 + 9/2 = 49/10.
MATHEMATICA
r[n_] := r[n] = If[n <= 2, 1/2, 1/r[n - 2] + r[n - 1]]; Numerator@ Array[r, 13] (* Michael De Vlieger, Jul 15 2017 *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
John Harmon, Jul 15 2017
STATUS
approved