a(n) = Fibonacci(n+1) - 2^floor(n/2).

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =1a(5) =4a(6) =5a(7) =13a(8) =18a(9) =39a(10) =57a(11) =112a(12) =169a(13) =313a(14) =482a(15) =859a(16) =1341a(17) =2328a(18) =3669a(19) =6253a(20) =9922a(21) =16687a(22) =26609a(23) =44320a(24) =70929a(25) =117297a(26) =188226a(27) =309619a(28) =497845a(29) =815656