Conjectured number of Lucas numbers with exactly n bits set in binary.
3, 2, 5, 1, 4, 4, 2, 0, 4, 3, 6, 1, 2, 1, 8, 0, 2, 1, 2, 2, 1, 4, 8, 1, 6, 3, 5, 5, 1, 2, 4, 2, 3, 3, 4, 1, 2, 4, 3, 3, 2, 3, 2, 2, 2, 4, 2, 9, 1, 2, 3, 5, 2, 3, 2, 1, 1, 1, 9, 1, 4, 2, 3, 1, 2, 6, 1, 4, 3, 5, 1, 3, 3, 5, 1, 3, 4, 3, 1, 3, 2, 5, 1, 5, 6, 1, 0
1
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
(Mma) f = LucasL[Range[0, 1000]]; Table[Length[Select[f, Total[IntegerDigits[#, 2]] == n &]], {n, 87}]
Cf. A000032 (Lucas numbers).
Cf. S000058 (Lucas numbers in binary), S000059 (Lucas numbers having n bits set).
nonn
T. D. Noe, May 19 2014