a(n) = Sum_{k=0..floor(n/2)} binomial(k+1,4*n-8*k+1).

Terms

a(0) =1a(1) =0a(2) =2a(3) =0a(4) =3a(5) =0a(6) =4a(7) =0a(8) =5a(9) =1a(10) =6a(11) =6a(12) =7a(13) =21a(14) =8a(15) =56a(16) =9a(17) =126a(18) =11a(19) =252a(20) =21a(21) =462a(22) =67a(23) =792a(24) =233a(25) =1287a(26) =729a(27) =2003a(28) =2017a(29) =3017