a(n) = Sum_{k=0..floor(n/3)} binomial(k+3,4*n-12*k+3).

Terms

a(0) =1a(1) =0a(2) =0a(3) =4a(4) =0a(5) =0a(6) =10a(7) =0a(8) =0a(9) =20a(10) =0a(11) =0a(12) =35a(13) =1a(14) =0a(15) =56a(16) =8a(17) =0a(18) =84a(19) =36a(20) =0a(21) =120a(22) =120a(23) =0a(24) =165a(25) =330a(26) =1a(27) =220a(28) =792a(29) =12