a(n) = (1 + 2^n + 3^n)/2.

Terms

a(0) =3a(1) =7a(2) =18a(3) =49a(4) =138a(5) =397a(6) =1158a(7) =3409a(8) =10098a(9) =30037a(10) =89598a(11) =267769a(12) =801258a(13) =2399677a(14) =7190838a(15) =21556129a(16) =64635618a(17) =193841317a(18) =581392878a(19) =1743916489a(20) =5231225178a(21) =15692626957a(22) =47075783718a(23) =141223156849a(24) =423661081938