n-th Lucas number (A000204(n)) + n-th non-Lucas number (A090946(n+1)).

Terms

a(0) =3a(1) =8a(2) =10a(3) =15a(4) =20a(5) =28a(6) =41a(7) =60a(8) =90a(9) =138a(10) =215a(11) =339a(12) =540a(13) =863a(14) =1385a(15) =2229a(16) =3594a(17) =5802a(18) =9374a(19) =15153a(20) =24503a(21) =39631a(22) =64109a(23) =103713a(24) =167793a(25) =271476a(26) =439238a(27) =710682a(28) =1149887a(29) =1860535