a(n) = Sum_{k=floor((n+1)/2)..n} Fibonacci(k+1).

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =10a(5) =16a(6) =29a(7) =47a(8) =81a(9) =131a(10) =220a(11) =356a(12) =589a(13) =953a(14) =1563a(15) =2529a(16) =4126a(17) =6676a(18) =10857a(19) =17567a(20) =28513a(21) =46135a(22) =74792a(23) =121016a(24) =196041a(25) =317201a(26) =513619a(27) =831053a(28) =1345282a(29) =2176712