a(n) = (1/3)*(Lucas(3*n) - Lucas(n)).

Terms

a(0) =1a(1) =5a(2) =24a(3) =105a(4) =451a(5) =1920a(6) =8149a(7) =34545a(8) =146376a(9) =620125a(10) =2626999a(11) =11128320a(12) =47140601a(13) =199691245a(14) =845906424a(15) =3583318305a(16) =15179181851a(17) =64300049280a(18) =272379384749