a(n) = Sum_{k=0..n} (-1)^k*k*Fibonacci(k), where Fibonacci(k) = A000045(k).

Terms

a(0) =0a(1) =-1a(2) =1a(3) =-5a(4) =7a(5) =-18a(6) =30a(7) =-61a(8) =107a(9) =-199a(10) =351a(11) =-628a(12) =1100a(13) =-1929a(14) =3349a(15) =-5801a(16) =9991a(17) =-17158a(18) =29354a(19) =-50085a(20) =85215a(21) =-144651a(22) =244991a(23) =-414120a(24) =698712a(25) =-1176913a(26) =1979305a(27) =-3323981a(28) =5574727a(29) =-9337914