Linear recurrence, with both signature and original terms = 1,0,1,0,1.

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =1a(5) =3a(6) =3a(7) =5a(8) =8a(9) =12a(10) =20a(11) =31a(12) =48a(13) =76a(14) =119a(15) =187a(16) =294a(17) =461a(18) =724a(19) =1137a(20) =1785a(21) =2803a(22) =4401a(23) =6910a(24) =10850a(25) =17036a(26) =26749a(27) =42000a(28) =65946a(29) =103545