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

Terms

a(0) =1a(1) =1a(2) =3a(3) =4a(4) =8a(5) =12a(6) =21a(7) =33a(8) =55a(9) =88a(10) =144a(11) =232a(12) =377a(13) =609a(14) =987a(15) =1596a(16) =2584a(17) =4180a(18) =6765a(19) =10945a(20) =17711a(21) =28656a(22) =46368a(23) =75024a(24) =121393a(25) =196417a(26) =317811a(27) =514228a(28) =832040a(29) =1346268