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

Terms

a(0) =1a(1) =0a(2) =0a(3) =-2a(4) =-2a(5) =-2a(6) =4a(7) =10a(8) =16a(9) =2a(10) =-32a(11) =-86a(12) =-90a(13) =26a(14) =332a(15) =646a(16) =534a(17) =-690a(18) =-3040a(19) =-4934a(20) =-2270a(21) =9066a(22) =27260a(23) =35198a(24) =532a(25) =-101946a(26) =-232752a(27) =-230730a(28) =158986a(29) =1039078