a(n) = (3^n + phi^(n-1) + (-phi)^(1-n)) / 5, where phi denotes the golden ratio A001622.

Terms

a(0) =0a(1) =1a(2) =2a(3) =6a(4) =17a(5) =50a(6) =148a(7) =441a(8) =1318a(9) =3946a(10) =11825a(11) =35454a(12) =106328a(13) =318929a(14) =956698a(15) =2869950a(16) =8609617a(17) =25828474a(18) =77484812a(19) =232453449a(20) =697358750a(21) =2092073666a(22) =6276216817a(23) =18828643686a(24) =56485920112a(25) =169457742625a(26) =508373199218