a(n) = Lucas(n) - floor(Lucas(n)/2).

Terms

a(0) =1a(1) =1a(2) =2a(3) =2a(4) =4a(5) =6a(6) =9a(7) =15a(8) =24a(9) =38a(10) =62a(11) =100a(12) =161a(13) =261a(14) =422a(15) =682a(16) =1104a(17) =1786a(18) =2889a(19) =4675a(20) =7564a(21) =12238a(22) =19802a(23) =32040a(24) =51841a(25) =83881a(26) =135722a(27) =219602a(28) =355324a(29) =574926