Forum Discussion

Viz's avatar
Viz
Brass Contributor
Jan 05, 2021

Lambda Example: Generate Fibonacci series

In this post, I would like to explain how I have used Lambda to create a function to generate a Fibonacci series array.   This example can also be used to understand how to create an array where th...
excel
office 365
Patrick2788's avatar
Patrick2788
Silver Contributor
Apr 24, 2023

I realize this solution is not the most efficient but it was fun to create and it's a bit different (Inspired by Pascal's Triangle).

 

 

'DiagonalSum
=LAMBDA(a,v,VSTACK(
    a,
    IF(v < 3, 1, SUM(IFERROR(COMBIN(SEQUENCE(v - 1, , v - 1, -1), SEQUENCE(v - 1, , 0)), 0)))
))

'Fib
=LAMBDA(elements,REDUCE(0, SEQUENCE(elements), DiagonalSum))

 

PeterBartholomew1's avatar
PeterBartholomew1
Silver Contributor
Apr 24, 2023

Patrick2788 

I think I am becoming conditioned!  I only have to read the words Pascal's triangle and I find myself writing

=REDUCE(1, SEQUENCE(n),
    LAMBDA(triangle, k,
        LET(
            previous, TAKE(triangle, -1),
            left,     HSTACK(previous, 0),
            right,    HSTACK(0, previous),
            IFNA(VSTACK(triangle, left + right), "")
        )
    )
)
  • Patrick2788's avatar
    Patrick2788
    Silver Contributor
    Apr 24, 2023

    PeterBartholomew1 

    Does that create a pyramid-like array?

     

    I went with a left-justified version:

    'Pascal
=Lambda(n,DROP(
    REDUCE(
        "",
        SEQUENCE(, n),
        LAMBDA(a, v, VSTACK(a, EXPAND(COMBIN(v - 1, SEQUENCE(, v, 0)), , n, "")))
    ),
    1
))
    • PeterBartholomew1's avatar
      PeterBartholomew1
      Silver Contributor
      Apr 25, 2023

      Patrick2788 

      No, like yours it is left stacked.  Far more effort would be required for they layout than was needed for the calculation!  The main difference is that mine is more primitive in that it uses the recurrence relation from row to row rather that the functional form of the result.

      Since you mention it though, how about this?

      = REDUCE(1, SEQUENCE(n),
    LAMBDA(triangle,k,
      LET(
        previous, TAKE(triangle, -1),
        left,     HSTACK(previous, {0,0}),
        right,    HSTACK({0,0}, previous),
        triangle, VSTACK(HSTACK(0,triangle), left + right),
        IFERROR(IF(triangle,triangle,""),"")
      )
    )
  )

       

      • Patrick2788's avatar
        Patrick2788
        Silver Contributor
        Apr 25, 2023
        It reads very well and is elegant. It's a different approach than I've been studying. Pascal's Triangle is fascinating because of the sub-arrays contained within. I had been working on something where the triangle would be created and the fibonacci numbers would be pulled from the sum of the 'shallow diagonals'. I had to stop myself because I was creating a problem that didn't need to exist when a more direct approach is better!

Resources