a(n) = F(n+1) + (1-(-1)^n)/2, where F() = Fibonacci numbers A000045.

Terms

a(0) =1a(1) =2a(2) =2a(3) =4a(4) =5a(5) =9a(6) =13a(7) =22a(8) =34a(9) =56a(10) =89a(11) =145a(12) =233a(13) =378a(14) =610a(15) =988a(16) =1597a(17) =2585a(18) =4181a(19) =6766a(20) =10946a(21) =17712a(22) =28657a(23) =46369a(24) =75025a(25) =121394a(26) =196418a(27) =317812a(28) =514229a(29) =832041