a(n) = Sum_{k=0..floor(n/2)} binomial(k,4*n-8*k).

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =1a(5) =0a(6) =1a(7) =0a(8) =1a(9) =1a(10) =1a(11) =5a(12) =1a(13) =15a(14) =1a(15) =35a(16) =1a(17) =70a(18) =2a(19) =126a(20) =10a(21) =210a(22) =46a(23) =330a(24) =166a(25) =495a(26) =496a(27) =716a(28) =1288a(29) =1014