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 to write an integer as the sum of Fibonacci numbers,
which are not necessarily distinct. This appears to be the first such asymptotic result
concerning partitions over Fibonacci numbers without the restriction to distinct
partitions. As well, under weak conditions, we prove analogous results for a general
linear recurrences.
