Fibonacci shuffles: a(2n) = A000071(n) and a(2n+1) = A001611(n+2).

Terms

a(0) =0a(1) =2a(2) =0a(3) =3a(4) =1a(5) =4a(6) =2a(7) =6a(8) =4a(9) =9a(10) =7a(11) =14a(12) =12a(13) =22a(14) =20a(15) =35a(16) =33a(17) =56a(18) =54a(19) =90a(20) =88a(21) =145a(22) =143a(23) =234a(24) =232a(25) =378a(26) =376a(27) =611a(28) =609a(29) =988