  We study the extended Frobenius problem for sequences of the form
$\{f_a+f_n\}_{n\in\mathbb{N}}$, where $\{f_n\}_{n\in\mathbb{N}}$ is the
Fibonacci sequence and $f_a$ is a Fibonacci number. As a consequence, we show
that the family of numerical semigroups associated to these sequences satisfies
the Wilf's conjecture.
