a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 2^(n-6k).

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =16a(5) =32a(6) =65a(7) =136a(8) =296a(9) =672a(10) =1584a(11) =3840a(12) =9473a(13) =23566a(14) =58736a(15) =146080a(16) =361760a(17) =891328a(18) =2184961a(19) =5331476a(20) =12958684a(21) =31400160a(22) =75910320a(23) =183220800a(24) =441787201a(25) =1064687642a(26) =2565404524a(27) =6181873208a(28) =14899796416a(29) =35922756992