a(n) = ((n+1)-st Fibonacci number) - (n-th non-Fibonacci number).

Terms

a(0) =-3a(1) =-4a(2) =-4a(3) =-4a(4) =-2a(5) =2a(6) =9a(7) =20a(8) =40a(9) =73a(10) =127a(11) =215a(12) =358a(13) =590a(14) =965a(15) =1574a(16) =2560a(17) =4156a(18) =6739a(19) =10919a(20) =17683a(21) =28628a(22) =46338a(23) =74994a(24) =121361a(25) =196385a(26) =317776a(27) =514193a(28) =832003a(29) =1346231