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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =4a(6) =6a(7) =9a(8) =13a(9) =20a(10) =32a(11) =51a(12) =82a(13) =133a(14) =215a(15) =346a(16) =555a(17) =886a(18) =1408a(19) =2231a(20) =3528a(21) =5572a(22) =8797a(23) =13892a(24) =21950a(25) =34707a(26) =54919a(27) =86958a(28) =137761a(29) =218339