a(n) = (7^n + 3^n - 2)/8.

Terms

a(0) =1a(1) =7a(2) =46a(3) =310a(4) =2131a(5) =14797a(6) =103216a(7) =721420a(8) =5046661a(9) =35316787a(10) =247187986a(11) =1730227330a(12) =12111325591a(13) =84778481977a(14) =593446982356