a(n) = 3^(n-3)*(binomial(n,3) + 3*binomial(n,2) + 9*n + 27).

Terms

a(0) =1a(1) =4a(2) =16a(3) =64a(4) =255a(5) =1008a(6) =3942a(7) =15228a(8) =58077a(9) =218700a(10) =813564a(11) =2991816a(12) =10884699a(13) =39208536a(14) =139946130a(15) =495303012a(16) =1739406393a(17) =6064804692a(18) =21006799848a(19) =72318491280a(20) =247561692471a(21) =843026984064