Step by Step solution about How to resolve the algorithm Padovan n-step number sequences step by step in the Julia programming language

Function nstep_Padovan:

• Purpose: Generates the first nterms terms of the first max_nstep 2..max_nstep-step Padovan sequences.

• Input Parameters:

  • max_nstep: Maximum step value for the Padovan sequences (default: 8).
  • nterms: Number of terms to generate for each step value (default: 15).

• Working:

  • Initializes a list start with empty sequences for n=0 and [1, 1, 1] for n=1 (hidden).
  • Iterates from n=2 to max_nstep:
    • Initializes this with the last n+1 terms from the previous step.
    • Extends this with new terms until it reaches nterms.
    • Appends this to the start list.

• Output: Returns a list containing the Padovan sequences for each step value from 2 to max_nstep.

Function print_Padovan_seq:

• Purpose: Prints the Padovan sequences in a table format.

• Input Parameter:

  • p: A list of Padovan sequences generated by nstep_Padovan.

• Working:

  • Prints a table header with columns for n and "Values."
  • Iterates through the Padovan sequences in the list:
    • Prints the step value n and the terms in the sequence, removing any non-numeric characters.
    • Adds a continuation mark (...) to indicate there may be more terms.
  • Closes the table.

In the main program:

• Calls the nstep_Padovan function to generate the Padovan sequences.
• Calls the print_Padovan_seq function to print the sequences in a table format.

Output:

• Prints a table containing the Padovan sequences for each step value from 2 to 8, with 15 terms per sequence. The table is formatted using CSS styles for alignment and coloring.

"""
    First nterms terms of the first 2..max_nstep -step Padovan sequences.
"""
function nstep_Padovan(max_nstep=8, nterms=15)
    start = [[], [1, 1, 1]]     # for n=0 and n=1 (hidden).
    for n in 2:max_nstep
        this = start[n][1:n+1]     # Initialise from last
        while length(this) < nterms
            push!(this, sum(this[end - i] for i in 1:n))
        end
        push!(start, this)
    end
    return start[3:end]
end

function print_Padovan_seq(p)
    println(strip("""
:::: {| style="text-align: left;" border="4" cellpadding="2" cellspacing="2"
|+ Padovan <math>n</math>-step sequences
|- style="background-color: rgb(255, 204, 255);"
! <math>n</math> !! Values
|-
          """))
    for (n, seq) in enumerate(p)
        println("| $n || $(replace(string(seq[2:end]), r"[ a-zA-Z\[\]]+" => "")), ...\n|-")
    end
    println("|}")
end

print_Padovan_seq(nstep_Padovan())