a(n) = Sum_{i=0..4} binomial(Fibonacci(n),i).

Terms

a(0) =1a(1) =2a(2) =2a(3) =4a(4) =8a(5) =31a(6) =163a(7) =1093a(8) =7547a(9) =52956a(10) =368831a(11) =2559196a(12) =17676661a(13) =121774888a(14) =837294004a(15) =5750356236a(16) =39462206694a(17) =270686172409