I've been working on a homework problem for an enumeration course that has been giving me fits.

Find a formula for f(n) if $\displaystyle \lambda(i) = \lfloor|sin(5i)|\rfloor\ \forall i \in N$.

$\displaystyle \Lambda (y) = \sum_{k\geq0}\lambda(k)y^k$

$\displaystyle F(x) = \Lambda (F(x))$

$\displaystyle F(x) = \sum_{i\geq0}\lfloor|sin(5i)|\rfloor F^i(x)$

Can anyone explain how I can find a power series representation of F(x) from which I can find f(n)?

Thanks.