Sum of Fibonacci(n)/Lucas(n)

[Jonathan Post]

Is there a seqfan who can tell me about this pair of sequences, which seems
not to be in OEIS?

a(n) = numerator(SUM[i=1..n]F(i)/L(i)) =
numerator(SUM[i=1..n]A000045(i)/A000032(i)).
b(n) = denominator(SUM[i=1..n]F(i)/L(i)) =
numerator(SUM[i=1..n]A000045(i)/A000032(i)).
The fractions, reduced to lowest terms, appear to begin:
0/2, 1/1, 4/3, 11/6, 95/42, 1255/462, 4381/1386, 7662223/1889118,
80819870/17946621, 3642636055/735811461, ...

Example: 0 + 1+1/3+2/4+3/7+5/11+8/18+13/29+21/47+34/76+55/123
= 1/1 <http://wims.unice.fr/wims/wims.cgi#>+
1/19<http://wims.unice.fr/wims/wims.cgi#>
+ 1/4 <http://wims.unice.fr/wims/wims.cgi#>+
1/1<http://wims.unice.fr/wims/wims.cgi#>
+ 1/13 <http://wims.unice.fr/wims/wims.cgi#>+
1/2<http://wims.unice.fr/wims/wims.cgi#>
+ 1/4 <http://wims.unice.fr/wims/wims.cgi#>+
1/1<http://wims.unice.fr/wims/wims.cgi#>
+ 1/6 <http://wims.unice.fr/wims/wims.cgi#>+
1/6<http://wims.unice.fr/wims/wims.cgi#>
+ 1/1 <http://wims.unice.fr/wims/wims.cgi#>+
1/85<http://wims.unice.fr/wims/wims.cgi#>
+ 1/1 <http://wims.unice.fr/wims/wims.cgi#>+
1/4<http://wims.unice.fr/wims/wims.cgi#>
+ 1/2 <http://wims.unice.fr/wims/wims.cgi#>
since the continued fractions and their convergents may matter.

After all the Fibonacci and Lucas-related seqs I've investigated, often with
expert help from OEIS editors, I ought to see this clearly, but do not. I'm
not even clear on the asymptotics.

Thanks.

-- Jonathan Vos Post
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