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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =11a(6) =22a(7) =43a(8) =85a(9) =171a(10) =351a(11) =738a(12) =1590a(13) =3498a(14) =7827a(15) =17757a(16) =40725a(17) =94113a(18) =218439a(19) =507852a(20) =1180395a(21) =2739312a(22) =6342084a(23) =14642100a(24) =33703182a(25) =77344686a(26) =176984406a(27) =403901722a(28) =919533655a(29) =2089000936