a(0)=0, a(n+1) is the least k>a(n) such that k+a(n)+n+1 is a Fibonacci number.

Terms

a(0) =0a(1) =1a(2) =2a(3) =3a(4) =6a(5) =10a(6) =18a(7) =30a(8) =51a(9) =84a(10) =139a(11) =227a(12) =371a(13) =603a(14) =980a(15) =1589a(16) =2576a(17) =4172a(18) =6756a(19) =10936a(20) =17701a(21) =28646a(22) =46357a(23) =75013a(24) =121381a(25) =196405a(26) =317798a(27) =514215a(28) =832026a(29) =1346254