a(n) = Lucas(n+1) - (n+1).

Terms

a(0) =1a(1) =1a(2) =3a(3) =6a(4) =12a(5) =22a(6) =39a(7) =67a(8) =113a(9) =188a(10) =310a(11) =508a(12) =829a(13) =1349a(14) =2191a(15) =3554a(16) =5760a(17) =9330a(18) =15107a(19) =24455a(20) =39581a(21) =64056a(22) =103658a(23) =167736a(24) =271417a(25) =439177a(26) =710619a(27) =1149822a(28) =1860468a(29) =3010318