a(n) = Lucas(4*n).

Terms

a(0) =2a(1) =7a(2) =47a(3) =322a(4) =2207a(5) =15127a(6) =103682a(7) =710647a(8) =4870847a(9) =33385282a(10) =228826127a(11) =1568397607a(12) =10749957122a(13) =73681302247a(14) =505019158607