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

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =13a(5) =31a(6) =61a(7) =151a(8) =413a(9) =1031a(10) =2445a(11) =5991a(12) =15069a(13) =37447a(14) =91917a(15) =226503a(16) =561373a(17) =1389735a(18) =3431501a(19) =8474983a(20) =20955229a(21) =51814407a(22) =128054029a(23) =316455559a(24) =782209629a(25) =1933537511a(26) =4779082829a(27) =11812031271a(28) =29195752157a(29) =72164132167