a(n) = C(n-1,1) + C(n-3,3) + ... + C(n-2*m-1,2*m+1), where m = floor((n-2)/4).

Terms

a(0) =1a(1) =2a(2) =3a(3) =4a(4) =6a(5) =10a(6) =17a(7) =28a(8) =45a(9) =72a(10) =116a(11) =188a(12) =305a(13) =494a(14) =799a(15) =1292a(16) =2090a(17) =3382a(18) =5473a(19) =8856a(20) =14329a(21) =23184a(22) =37512a(23) =60696a(24) =98209a(25) =158906a(26) =257115a(27) =416020a(28) =673134a(29) =1089154