a(n) = (n^2 + 3*n + 10/3)*4^(n-3) - 1/3.

Terms

a(0) =3a(1) =21a(2) =125a(3) =693a(4) =3669a(5) =18773a(6) =93525a(7) =456021a(8) =2184533a(9) =10310997a(10) =48059733a(11) =221599061a(12) =1012225365a(13) =4585772373a(14) =20624790869a(15) =92162839893a(16) =409453548885