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

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =1a(5) =1a(6) =1a(7) =3a(8) =1a(9) =6a(10) =2a(11) =10a(12) =6a(13) =15a(14) =16a(15) =22a(16) =36a(17) =35a(18) =71a(19) =64a(20) =128a(21) =129a(22) =220a(23) =265a(24) =376a(25) =529a(26) =661a(27) =1013a(28) =1211a(29) =1873