a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n-1-3*k,n-4*k) * binomial(2*k,k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =-2a(5) =-2a(6) =-2a(7) =-2a(8) =4a(9) =10a(10) =16a(11) =22a(12) =8a(13) =-26a(14) =-80a(15) =-154a(16) =-178a(17) =-82a(18) =204a(19) =750a(20) =1374a(21) =1642a(22) =868a(23) =-1886a(24) =-6886a(25) =-12802a(26) =-15784a(27) =-8538a(28) =17166a(29) =64554