a(n) = ((5+sqrt(5))/2)^n + ((5-sqrt(5))/2)^n.

Terms

a(0) =2a(1) =5a(2) =15a(3) =50a(4) =175a(5) =625a(6) =2250a(7) =8125a(8) =29375a(9) =106250a(10) =384375a(11) =1390625a(12) =5031250a(13) =18203125a(14) =65859375a(15) =238281250a(16) =862109375a(17) =3119140625a(18) =11285156250a(19) =40830078125a(20) =147724609375a(21) =534472656250