a(n)=(-1)^C(n+1,2)*(F(n+1)*(1+(-1)^n)/2+F(n+2)*(1-(-1)^n)/2).

Terms

a(0) =1a(1) =-2a(2) =-2a(3) =5a(4) =5a(5) =-13a(6) =-13a(7) =34a(8) =34a(9) =-89a(10) =-89a(11) =233a(12) =233a(13) =-610a(14) =-610a(15) =1597a(16) =1597a(17) =-4181a(18) =-4181a(19) =10946a(20) =10946a(21) =-28657a(22) =-28657a(23) =75025a(24) =75025a(25) =-196418a(26) =-196418a(27) =514229a(28) =514229a(29) =-1346269