a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k-1,k) * binomial(k,n-4*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =0a(5) =1a(6) =0a(7) =0a(8) =0a(9) =2a(10) =3a(11) =0a(12) =0a(13) =3a(14) =12a(15) =10a(16) =0a(17) =4a(18) =30a(19) =60a(20) =35a(21) =5a(22) =60a(23) =210a(24) =280a(25) =132a(26) =105a(27) =560a(28) =1260a(29) =1267