a(n) = ceiling(Fibonacci(n)/3).

Terms

a(0) =0a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =3a(7) =5a(8) =7a(9) =12a(10) =19a(11) =30a(12) =48a(13) =78a(14) =126a(15) =204a(16) =329a(17) =533a(18) =862a(19) =1394a(20) =2255a(21) =3649a(22) =5904a(23) =9553a(24) =15456a(25) =25009a(26) =40465a(27) =65473a(28) =105937a(29) =171410