a(n) = b(n) + d(n), where b(n) = (n-th Lucas number > 3) and d(n) = (n-th non-Fibonacci number).

Terms

a(0) =8a(1) =13a(2) =18a(3) =27a(4) =39a(5) =58a(6) =88a(7) =137a(8) =214a(9) =338a(10) =538a(11) =861a(12) =1383a(13) =2227a(14) =3593a(15) =5801a(16) =9373a(17) =15152a(18) =24502a(19) =39630a(20) =64107a(21) =103711a(22) =167791a(23) =271474a(24) =439236a(25) =710680a(26) =1149886a(27) =1860534a(28) =3010386a(29) =4870885