a(n) = floor((-1 + 4^n)/(-1 + 3*n)).

Terms

a(0) =1a(1) =3a(2) =7a(3) =23a(4) =73a(5) =240a(6) =819a(7) =2849a(8) =10082a(9) =36157a(10) =131071a(11) =479349a(12) =1766022a(13) =6547206a(14) =24403223a(15) =91382282a(16) =343597383a(17) =1296593900a(18) =4908534052a(19) =18635790301a(20) =70936234050a(21) =270649016067