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

Terms

a(0) =1a(1) =0a(2) =2a(3) =0a(4) =3a(5) =0a(6) =4a(7) =1a(8) =5a(9) =5a(10) =6a(11) =15a(12) =7a(13) =35a(14) =9a(15) =70a(16) =17a(17) =126a(18) =46a(19) =210a(20) =131a(21) =331a(22) =342a(23) =506a(24) =805a(25) =781a(26) =1730a(27) =1287a(28) =3448a(29) =2366