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

Terms

a(0) =1a(1) =0a(2) =2a(3) =1a(4) =5a(5) =5a(6) =15a(7) =20a(8) =50a(9) =76a(10) =176a(11) =286a(12) =638a(13) =1078a(14) =2354a(15) =4081a(16) =8789a(17) =15521a(18) =33099a(19) =59279a(20) =125477a(21) =227239a(22) =478193a(23) =873885a(24) =1830271a(25) =3370029a(26) =7030571a(27) =13027729a(28) =27088871a(29) =50469889