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 A303655 Bit column sums in the binary expansions of Fibonacci(n)/2^n for n >= 1. 1
 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, 29, 32, 34, 32, 37, 34, 33, 43, 30, 37, 41, 46, 43, 44, 42, 52, 45, 51, 50, 53, 50, 51, 49, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..800 from Paul D. Hanna) FORMULA Sum_{n>=1} a(n) / 2^n = 2. EXAMPLE The binary expansions of Fibonacci(n)/2^n for n >= 1 begin: .1 .01 .010 .0011 .00101 .001000 .0001101 .00010101 .000100010 .0000110111 .00001011001 .000010010000 .0000011101001 .00000101111001 .000001001100010 .0000001111011011 .00000011000111101 .000000101000011000 .0000001000001010101 .00000001101001101101 .000000010101011000010 .0000000100010100101111 .00000000110111111110001 .000000001011010100100000 .0000000010010010100010001 .00000000011101101000110001 .000000000101111111101000010 .0000000001001101100101110011 .00000000001111101100010110101 .000000000011001011001000101000 .0000000000101001000101011011101 .00000000001000010011110100000101 .000000000001101011100011111100010 .0000000000010101110000010011100111 .00000000000100011001100110011001001 .000000000000111000111101000110110000 .0000000000001011100001001111001111001 .00000000000010010101000111000000101001 .000000000000011110001010000111010100010 .0000000000000110000110010111111011001011 .00000000000001001110111101000110101101101 .000000000000001111111110000000110000111000 .0000000000000011001110101101001100110100101 .00000000000000101001110011101010010111011101 .000000000000001000011101001010011111110000010 .0000000000000001101101011100111110010101011111 .00000000000000010110001000110010010010011100001 .000000000000000100011110100011010000101001000000 .0000000000000000111001111101001100010111100100001 .00000000000000001011101110001100110011100101100001 ... the column sums of which form this sequence. Thus, a(n) equals the number of 1-bits in column n in the binary expansions of Fibonacci(n)/2^n for n >= 1. CROSSREFS Cf. A000045, A037093. Sequence in context: A094017 A092762 A017844 * A011156 A213478 A266449 Adjacent sequences:  A303652 A303653 A303654 * A303656 A303657 A303658 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 27 2018 STATUS approved

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Last modified October 21 13:57 EDT 2019. Contains 328299 sequences. (Running on oeis4.)