a(n) = (8^n - 7^n - 6^n - 5^n + 4*4^n)/2.

Terms

a(0) =1a(1) =3a(2) =9a(3) =42a(4) =399a(5) =4578a(6) =49299a(7) =490542a(8) =4602159a(9) =41440938a(10) =362614539a(11) =3108879942a(12) =26262187719a(13) =219426920898