a(n) = Sum_{k <= n/2 } binomial(n-2k, 3k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =5a(7) =11a(8) =21a(9) =36a(10) =58a(11) =92a(12) =149a(13) =250a(14) =431a(15) =750a(16) =1299a(17) =2227a(18) =3784a(19) =6401a(20) =10828a(21) =18364a(22) =31236a(23) =53228a(24) =90741a(25) =154603a(26) =263178a(27) =447702a(28) =761403a(29) =1295022