a(n) = ((n+1)-st Lucas number) - (n-th non-Lucas number).

Terms

a(0) =-2a(1) =-2a(2) =-1a(3) =2a(4) =8a(5) =17a(6) =34a(7) =62a(8) =108a(9) =183a(10) =305a(11) =502a(12) =823a(13) =1343a(14) =2185a(15) =3548a(16) =5754a(17) =9324a(18) =15101a(19) =24449a(20) =39575a(21) =64049a(22) =103651a(23) =167729a(24) =271410a(25) =439170a(26) =710612a(27) =1149815a(28) =1860461a(29) =3010311