a(n) = Sum_{k=0..floor(n/4)} binomial(n-2k,2k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =4a(6) =7a(7) =11a(8) =17a(9) =27a(10) =44a(11) =72a(12) =117a(13) =189a(14) =305a(15) =493a(16) =798a(17) =1292a(18) =2091a(19) =3383a(20) =5473a(21) =8855a(22) =14328a(23) =23184a(24) =37513a(25) =60697a(26) =98209a(27) =158905a(28) =257114a(29) =416020