a(n) = Sum_{k=0..floor(n/3)} C(n-k, 2*k) * 2^k*3^(n-3*k).

Terms

a(0) =1a(1) =3a(2) =9a(3) =29a(4) =99a(5) =351a(6) =1273a(7) =4677a(8) =17307a(9) =64295a(10) =239361a(11) =892125a(12) =3327091a(13) =12412143a(14) =46313289a(15) =172824629a(16) =644952459a(17) =2406919671a(18) =8982595153a(19) =33523198797a(20) =125109675747a(21) =466914455615