a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2*n-4*k+1,2*k+1).

Terms

a(0) =1a(1) =3a(2) =5a(3) =9a(4) =29a(5) =81a(6) =185a(7) =429a(8) =1093a(9) =2785a(10) =6817a(11) =16613a(12) =41181a(13) =102441a(14) =253049a(15) =623693a(16) =1541557a(17) =3814929a(18) =9430545a(19) =23297397a(20) =57577997a(21) =142345721a(22) =351858985a(23) =869614109a(24) =2149341925a(25) =5312698977a(26) =13131636417a(27) =32457015109a(28) =80223121469a(29) =198288112969