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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =3a(6) =4a(7) =6a(8) =9a(9) =13a(10) =19a(11) =28a(12) =41a(13) =61a(14) =93a(15) =144a(16) =226a(17) =359a(18) =574a(19) =920a(20) =1475a(21) =2361a(22) =3769a(23) =6000a(24) =9528a(25) =15100a(26) =23897a(27) =37789a(28) =59739a(29) =94446