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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =0a(5) =-1a(6) =-2a(7) =-3a(8) =-2a(9) =1a(10) =6a(11) =13a(12) =17a(13) =13a(14) =-4a(15) =-39a(16) =-83a(17) =-113a(18) =-92a(19) =31a(20) =279a(21) =605a(22) =850a(23) =701a(24) =-219a(25) =-2129a(26) =-4736a(27) =-6749a(28) =-5690a(29) =1569