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

Terms

a(0) =1a(1) =2a(2) =3a(3) =4a(4) =9a(5) =26a(6) =63a(7) =128a(8) =241a(9) =486a(10) =1075a(11) =2412a(12) =5189a(13) =10770a(14) =22343a(15) =47352a(16) =101801a(17) =218142a(18) =462635a(19) =976260a(20) =2065741a(21) =4391914a(22) =9351823a(23) =19877904a(24) =42164785a(25) =89409718a(26) =189779059a(27) =403162268a(28) =856453269a(29) =1818474626