A165277 Number of odd-indexed Fibonacci numbers in the Zeckendorf representation of n.

0, 1, 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 1, 2, 2, 3, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 3, 2, 2, 3, 3, 4, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 1, 2, 2, 3, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 3, 2

Offset: 1

Author

Clark Kimberling, Sep 12 2009

Keywords

• nonn

Comments

We begin the indexing at 2; that is, 1=F(2), 2=F(3), 3=F(4), 5=F(5), ...

For a count of even-indexed Fibonacci summands, see A165276.

Examples

			6 = 5 + 1 = F(5) + F(2), so that a(6) = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014417, A165276, A165278, A165279.

Programs

Mathematica

fibOddCount[n_] := Plus @@ (Reverse@IntegerDigits[n, 2])[[2 ;; -1 ;; 2]]; fibOddCount /@ Select[Range[1000], BitAnd[#, 2 #] == 0 &] (* Amiram Eldar, Jan 20 2020 *)