A050170 a(n)=[ A/sqrt(5) ] if this is not in {0,a(1),...,a(n-1)}, else a(n)=[ A*sqrt(5) ], where A=a(n-1).

1, 2, 4, 8, 3, 6, 13, 5, 11, 24, 10, 22, 9, 20, 44, 19, 42, 18, 40, 17, 7, 15, 33, 14, 31, 69, 30, 67, 29, 12, 26, 58, 25, 55, 122, 54, 120, 53, 23, 51, 114, 50, 111, 49, 21, 46, 102, 45, 100, 223, 99, 221, 98, 43, 96, 214, 95, 212, 94, 210