a(n) = floor((3*4^n + 2*3^n)/5).

Terms

a(0) =1a(1) =3a(2) =13a(3) =49a(4) =186a(5) =711a(6) =2749a(7) =10705a(8) =41946a(9) =165159a(10) =652765a(11) =2587441a(12) =10278906a(13) =40903047a(14) =162974461a(15) =649984657a(16) =2594199066a(17) =10359577575a(18) =41386654237a(19) =165391648753a(20) =661101690426