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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...
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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,""),"")
      )
    )
  )

         

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