%I #16 Apr 28 2018 00:49:18
%S 1,2,3,4,5,5,7,12,9,10,9,14,13,18,21,17,23,16,20,24,23,23,26,26,30,29,
%T 29,32,34,32,37,34,33,43,30,37,41,46,43,44,42,52,45,51,50,53,50,51,49,
%U 55,64,48,60,53,65,73,67,58,69,62,75,65,74,71,69,68,88,89,85,67,76,82,83,76,81,89,91,98,93,92,83,104,87,95,90,85,101,91,101,105,105,114,84,104,108,116,121,104,126,104,110,131,107,111,137,109,126,124,119,127,136,127,120,122,145,132,132,127,131,122,129,130,136,144,146
%N Bit column sums in the binary expansions of Fibonacci(n)/2^n for n >= 1.
%H Chai Wah Wu, <a href="/A303655/b303655.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..800 from Paul D. Hanna)
%F Sum_{n>=1} a(n) / 2^n = 2.
%e The binary expansions of Fibonacci(n)/2^n for n >= 1 begin:
%e .1
%e .01
%e .010
%e .0011
%e .00101
%e .001000
%e .0001101
%e .00010101
%e .000100010
%e .0000110111
%e .00001011001
%e .000010010000
%e .0000011101001
%e .00000101111001
%e .000001001100010
%e .0000001111011011
%e .00000011000111101
%e .000000101000011000
%e .0000001000001010101
%e .00000001101001101101
%e .000000010101011000010
%e .0000000100010100101111
%e .00000000110111111110001
%e .000000001011010100100000
%e .0000000010010010100010001
%e .00000000011101101000110001
%e .000000000101111111101000010
%e .0000000001001101100101110011
%e .00000000001111101100010110101
%e .000000000011001011001000101000
%e .0000000000101001000101011011101
%e .00000000001000010011110100000101
%e .000000000001101011100011111100010
%e .0000000000010101110000010011100111
%e .00000000000100011001100110011001001
%e .000000000000111000111101000110110000
%e .0000000000001011100001001111001111001
%e .00000000000010010101000111000000101001
%e .000000000000011110001010000111010100010
%e .0000000000000110000110010111111011001011
%e .00000000000001001110111101000110101101101
%e .000000000000001111111110000000110000111000
%e .0000000000000011001110101101001100110100101
%e .00000000000000101001110011101010010111011101
%e .000000000000001000011101001010011111110000010
%e .0000000000000001101101011100111110010101011111
%e .00000000000000010110001000110010010010011100001
%e .000000000000000100011110100011010000101001000000
%e .0000000000000000111001111101001100010111100100001
%e .00000000000000001011101110001100110011100101100001
%e ...
%e the column sums of which form this sequence.
%e Thus, a(n) equals the number of 1-bits in column n in the binary expansions of Fibonacci(n)/2^n for n >= 1.
%Y Cf. A000045, A037093.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Apr 27 2018