a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 2^(n-5k).

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =16a(5) =32a(6) =66a(7) =144a(8) =336a(9) =832a(10) =2144a(11) =5632a(12) =14852a(13) =38968a(14) =101312a(15) =260736a(16) =664704a(17) =1681152a(18) =4226056a(19) =10578080a(20) =26407648a(21) =65838848a(22) =164095360a(23) =409129472a(24) =1020795408a(25) =2549137824a(26) =6371133120a(27) =15935185792a(28) =39878810624a(29) =99837958144