a(n) = Sum_{k=0..floor(n/4)} C(n-k,3*k) * 2^(n-3*k).

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =18a(5) =48a(6) =144a(7) =448a(8) =1380a(9) =4152a(10) =12224a(11) =35456a(12) =102024a(13) =292768a(14) =840416a(15) =2416384a(16) =6959504a(17) =20069280a(18) =57913536a(19) =167158656a(20) =482462752a(21) =1392319488a(22) =4017460224a(23) =11590946816a(24) =33439639616a(25) =96470796672a(26) =278311599616