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

Terms

a(0) =1a(1) =2a(2) =6a(3) =19a(4) =64a(5) =215a(6) =744a(7) =2621a(8) =9362a(9) =33825a(10) =123361a(11) =453438a(12) =1677721a(13) =6242685a(14) =23342213a(15) =87652393a(16) =330382099a(17) =1249445031a(18) =4739274257a(19) =18024780783a(20) =68719476736a(21) =262569940961