a(n) = Sum_{k == floor(n/2) (mod 5)} C(n,k).

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =10a(6) =20a(7) =35a(8) =70a(9) =127a(10) =254a(11) =474a(12) =948a(13) =1807a(14) =3614a(15) =6995a(16) =13990a(17) =27370a(18) =54740a(19) =107883a(20) =215766a(21) =427351a(22) =854702a(23) =1698458a(24) =3396916a(25) =6765175a(26) =13530350a(27) =26985675a(28) =53971350a(29) =107746282