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We know that the Fibonacci (or Virahanka) numbers can be used to count how many ways to express each integer as a sum of 1s and 2s:
1=1 (1 way)
2=1+1=2 (2 ways)
3=1+1+1=1+2=2+1 (3 ways)
4=1+1+1+1=1+1+2=1+2+1=2+1+1=2+2 (5 ways)
5=1+1+1+1+1=1+1+1+2=1+1+2+1=1+2+1+1=1+2+2=2+1+1+1=2+1+2=2+2+1 (8 ways)
and so on. But what if we want to count the number of terms used in all these sums, or (equivalently) the average number of terms, or (again, equivalently) the average ratio of 1s to 2s? That’s the problem addressed in this post.
https://thalestriangles.blogspot.com/2023/03/an-average-number-of-1s-and-2s.html
#math #Fibonacci #Virahanka