

A011373


Number of 1's in binary expansion of Fibonacci(n).


4



0, 1, 1, 1, 2, 2, 1, 3, 3, 2, 5, 4, 2, 5, 6, 4, 8, 7, 4, 5, 8, 6, 8, 11, 6, 6, 9, 11, 11, 12, 8, 11, 9, 13, 12, 11, 12, 14, 10, 12, 16, 17, 14, 16, 18, 15, 21, 13, 12, 18, 18, 17, 17, 17, 16, 22, 21, 16, 24, 20, 16, 19, 26, 23, 20, 25, 19, 26, 15, 23, 23, 22, 25, 27, 24, 23, 23, 22
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OFFSET

0,5


LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000
Index entries for sequences related to binary expansion of n


FORMULA

a(n) = A000120(A000045(n)).  Michel Marcus, Dec 27 2014
a(n) = [x^Fibonacci(n)] (1/(1  x))*Sum_{k>=0} x^(2^k)/(1 + x^(2^k)).  Ilya Gutkovskiy, Mar 27 2018


EXAMPLE

a(8) = 3 because Fibonacci(8) = 21, which in binary is 11001 and that has 3 on bits.
a(9) = 2 because Fibonacci(9) = 34, which in binary is 100010 and that only has 2 on bits.


MAPLE

A000120 := proc(n) add(d, d=convert(n, base, 2)) ; end proc:
A011373 := proc(n) A000120(combinat[fibonacci](n)) ; end proc:
seq(A011373(n), n=0..50) ; # R. J. Mathar, Mar 22 2011


MATHEMATICA

DigitCount[#, 2, 1]&/@Fibonacci[Range[0, 79]] (* Harvey P. Dale, Mar 14 2011 *)
Table[Plus@@IntegerDigits[Fibonacci[n], 2], {n, 0, 79}]


PROG

(PARI) a(n)=hammingweight(fibonacci(n)) \\ Charles R Greathouse IV, Mar 02 2014


CROSSREFS

Cf. A000045, A000120, A059016.
Sequence in context: A029266 A035387 A242308 * A177352 A210798 A117915
Adjacent sequences: A011370 A011371 A011372 * A011374 A011375 A011376


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane


STATUS

approved



