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

Terms

a(0) =5a(1) =9a(2) =11a(3) =16a(4) =21a(5) =29a(6) =41a(7) =61a(8) =91a(9) =139a(10) =216a(11) =340a(12) =540a(13) =863a(14) =1386a(15) =2230a(16) =3595a(17) =5803a(18) =9375a(19) =15154a(20) =24504a(21) =39632a(22) =64109a(23) =103713a(24) =167793a(25) =271476a(26) =439239a(27) =710683a(28) =1149888a(29) =1860536