a(n) = 2^n + Fibonacci(n+1).

Terms

a(0) =2a(1) =3a(2) =6a(3) =11a(4) =21a(5) =40a(6) =77a(7) =149a(8) =290a(9) =567a(10) =1113a(11) =2192a(12) =4329a(13) =8569a(14) =16994a(15) =33755a(16) =67133a(17) =133656a(18) =266325a(19) =531053a(20) =1059522a(21) =2114863a(22) =4222961a(23) =8434976a(24) =16852241a(25) =33675825a(26) =67305282a(27) =134535539a(28) =268949685a(29) =537702952