a(n) = 3^n*Lucas(n), where Lucas = A000204.

Terms

a(0) =3a(1) =27a(2) =108a(3) =567a(4) =2673a(5) =13122a(6) =63423a(7) =308367a(8) =1495908a(9) =7263027a(10) =35252253a(11) =171124002a(12) =830642283a(13) =4032042867a(14) =19571909148a(15) =95004113247a(16) =461159522073