a(n) = Lucas(4n)+2 = Lucas(2n)^2.

Terms

a(0) =4a(1) =9a(2) =49a(3) =324a(4) =2209a(5) =15129a(6) =103684a(7) =710649a(8) =4870849a(9) =33385284a(10) =228826129a(11) =1568397609a(12) =10749957124a(13) =73681302249a(14) =505019158609