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

Terms

a(0) =0a(1) =1a(2) =4a(3) =13a(4) =39a(5) =112a(6) =313a(7) =859a(8) =2328a(9) =6253a(10) =16687a(11) =44320a(12) =117297a(13) =309619a(14) =815656a(15) =2145541a(16) =5637351a(17) =14799280a(18) =38826025a(19) =101809867a(20) =266865720a(21) =699311581a(22) =1832117599a(23) =4799138368a(24) =12569491809a(25) =32917725667a(26) =86200462408a(27) =225717215989a(28) =591018294423