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

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =18a(5) =44a(6) =112a(7) =288a(8) =740a(9) =1896a(10) =4848a(11) =12384a(12) =31624a(13) =80752a(14) =206208a(15) =526592a(16) =1344784a(17) =3434272a(18) =8770368a(19) =22397568a(20) =57198368a(21) =146071744a(22) =373034240a(23) =952645120a(24) =2432840256a(25) =6212924032a(26) =15866403584a(27) =40519208448a(28) =103476899968