login
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
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
Sequence in context: A092762 A017844 A377482 * A011156 A213478 A332782
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 27 2018
STATUS
approved