a(n) = (4^n + 5)/3.

Terms

a(0) =2a(1) =3a(2) =7a(3) =23a(4) =87a(5) =343a(6) =1367a(7) =5463a(8) =21847a(9) =87383a(10) =349527a(11) =1398103a(12) =5592407a(13) =22369623a(14) =89478487a(15) =357913943a(16) =1431655767a(17) =5726623063a(18) =22906492247a(19) =91625968983a(20) =366503875927