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| View Original: | Binary and generalized Fibonacci numbers - no composition addend divisible by 2 (Fibonacci numbers).svg (259x11) | |||
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| Keywords: Binary and generalized Fibonacci numbers - no composition addend divisible by 2 (Fibonacci numbers).svg Binary and generalized Fibonacci numbers - no composition addend divisible by 2 Fibonacci numbers svg 3000px Quote from A000045 F n number of compositions of n into odd parts; e g F 6 counts 1+1+1+1+1+1 1+1+1+3 1+1+3+1 1+3+1+1 1+5 3+1+1+1 3+3 5+1 Due to the bijection between compositions<br> 500px<br> this can be expressed in terms of binary numbers Odd composition addends 1s match the space between binary 0s the space left of leftmost 0s the space right of rightmost 0s 3s 5s 7s 9s match blocks of binary 1s of length 2 4 6 8 These blocks corresponding to odd composition addends are marked in strong red Columns without even composition addents i e without light red squares are marked by a black dot Counting these black dots from left side to a green trigon gives a Fibonacci number own mate2code Binary and generalized Fibonacci numbers | ||||
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