a(n) = Sum_{k=0..floor(n/3)} binomial(k+1,2*n-6*k+1).

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =0a(5) =0a(6) =3a(7) =1a(8) =0a(9) =4a(10) =4a(11) =0a(12) =5a(13) =10a(14) =1a(15) =6a(16) =20a(17) =6a(18) =7a(19) =35a(20) =21a(21) =9a(22) =56a(23) =56a(24) =17a(25) =84a(26) =126a(27) =46a(28) =121a(29) =252