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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =5a(5) =11a(6) =19a(7) =29a(8) =69a(9) =163a(10) =341a(11) =639a(12) =1319a(13) =2913a(14) =6343a(15) =13061a(16) =27029a(17) =57699a(18) =124813a(19) =265583a(20) =560385a(21) =1191233a(22) =2557743a(23) =5486007a(24) =11713623a(25) =25013061a(26) =53632099a(27) =115219909a(28) =247312763a(29) =530489403