This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A303655 #16 Apr 28 2018 00:49:18 %S A303655 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 A303655 29,32,34,32,37,34,33,43,30,37,41,46,43,44,42,52,45,51,50,53,50,51,49, %U A303655 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 A303655 Bit column sums in the binary expansions of Fibonacci(n)/2^n for n >= 1. %H A303655 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 A303655 Sum_{n>=1} a(n) / 2^n = 2. %e A303655 The binary expansions of Fibonacci(n)/2^n for n >= 1 begin: %e A303655 .1 %e A303655 .01 %e A303655 .010 %e A303655 .0011 %e A303655 .00101 %e A303655 .001000 %e A303655 .0001101 %e A303655 .00010101 %e A303655 .000100010 %e A303655 .0000110111 %e A303655 .00001011001 %e A303655 .000010010000 %e A303655 .0000011101001 %e A303655 .00000101111001 %e A303655 .000001001100010 %e A303655 .0000001111011011 %e A303655 .00000011000111101 %e A303655 .000000101000011000 %e A303655 .0000001000001010101 %e A303655 .00000001101001101101 %e A303655 .000000010101011000010 %e A303655 .0000000100010100101111 %e A303655 .00000000110111111110001 %e A303655 .000000001011010100100000 %e A303655 .0000000010010010100010001 %e A303655 .00000000011101101000110001 %e A303655 .000000000101111111101000010 %e A303655 .0000000001001101100101110011 %e A303655 .00000000001111101100010110101 %e A303655 .000000000011001011001000101000 %e A303655 .0000000000101001000101011011101 %e A303655 .00000000001000010011110100000101 %e A303655 .000000000001101011100011111100010 %e A303655 .0000000000010101110000010011100111 %e A303655 .00000000000100011001100110011001001 %e A303655 .000000000000111000111101000110110000 %e A303655 .0000000000001011100001001111001111001 %e A303655 .00000000000010010101000111000000101001 %e A303655 .000000000000011110001010000111010100010 %e A303655 .0000000000000110000110010111111011001011 %e A303655 .00000000000001001110111101000110101101101 %e A303655 .000000000000001111111110000000110000111000 %e A303655 .0000000000000011001110101101001100110100101 %e A303655 .00000000000000101001110011101010010111011101 %e A303655 .000000000000001000011101001010011111110000010 %e A303655 .0000000000000001101101011100111110010101011111 %e A303655 .00000000000000010110001000110010010010011100001 %e A303655 .000000000000000100011110100011010000101001000000 %e A303655 .0000000000000000111001111101001100010111100100001 %e A303655 .00000000000000001011101110001100110011100101100001 %e A303655 ... %e A303655 the column sums of which form this sequence. %e A303655 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 A303655 Cf. A000045, A037093. %K A303655 nonn %O A303655 1,2 %A A303655 _Paul D. Hanna_, Apr 27 2018