a(n) = Sum_{k=0..floor(n/4)} 2^k * binomial(2*n-6*k+1,2*k+1).

Terms

a(0) =1a(1) =3a(2) =5a(3) =7a(4) =11a(5) =31a(6) =83a(7) =183a(8) =351a(9) =675a(10) =1435a(11) =3231a(12) =7119a(13) =14987a(14) =30963a(15) =64871a(16) =138775a(17) =298403a(18) =636091a(19) =1344191a(20) =2838399a(21) =6021371a(22) =12818467a(23) =27277207a(24) =57911207a(25) =122790675a(26) =260485131a(27) =553185519a(28) =1175285967a(29) =2496108459