a(n) = b(n) + d(n), where b(n) = (n-th Fibonacci number > 1) and d(n) = (n-th non-Lucas number).

Terms

a(0) =4a(1) =8a(2) =11a(3) =16a(4) =22a(5) =31a(6) =46a(7) =68a(8) =103a(9) =159a(10) =249a(11) =394a(12) =629a(13) =1007a(14) =1618a(15) =2606a(16) =4204a(17) =6789a(18) =10971a(19) =17737a(20) =28684a(21) =46396a(22) =75055a(23) =121424a(24) =196450a(25) =317844a(26) =514263a(27) =832075a(28) =1346305a(29) =2178346