a(n) = b(n) + d(n), where b(n) = (n-th Fibonacci number > 2) and d(n) = (n-th non-Lucas number).

Terms

a(0) =5a(1) =10a(2) =14a(3) =21a(4) =30a(5) =44a(6) =67a(7) =102a(8) =158a(9) =248a(10) =393a(11) =627a(12) =1006a(13) =1617a(14) =2605a(15) =4203a(16) =6788a(17) =10970a(18) =17736a(19) =28683a(20) =46395a(21) =75053a(22) =121423a(23) =196449a(24) =317843a(25) =514262a(26) =832074a(27) =1346304a(28) =2178345a(29) =3524615