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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =5a(6) =11a(7) =22a(8) =43a(9) =85a(10) =170a(11) =341a(12) =683a(13) =1367a(14) =2744a(15) =5552a(16) =11381a(17) =23729a(18) =50423a(19) =109220a(20) =240845a(21) =539411a(22) =1223357a(23) =2800535a(24) =6451340a(25) =14915084a(26) =34533851a(27) =79949741a(28) =184865936a(29) =426627122