  In this paper, harkening back to ideas of Hardy and Ramanujan, Mahler and de
Bruijn, with the addition of more recent results on the Fibonacci Dirichlet
series, we determine the asymptotic number of ways $p_F(n)$ to write an integer
as the sum of non-distinct Fibonacci numbers. This appears to be the first such
asymptotic result concerning non-distinct partitions over Fibonacci numbers. As
well, under weak conditions, we prove analogous results for a general linear
recurrences.
