Padovan sequence: Difference between revisions

=={{header|MATLAB}}==

<syntaxhighlight lang="MATLAB">clear all;close all;clc;

% Calculate the sequences

padovan_sequence_20 = Padovan1(20)

padovan_approx_20 = Padovan2(20)

% Check if the sequences are equal for n = 64

are_sequences_equal = isequal(Padovan1(64), Padovan2(64))

% Generate the substitution system sequence

sequence_32 = createLSystem();

words = sequence_32(1:10)

% Check if the length of the substitution system sequence equals the Padovan sequence

are_lengths_equal = all( cellfun(@(ele) length(ele), sequence_32) ...

== Padovan2(32) )

function words = createLSystem()

words = {'A'}; % Initialize cell array with one element "A"

text = 'A'; % Current text is "A"

while length(words) < 32

newText = ''; % Initialize new text as empty

for i = 1:length(text)

switch text(i)

case 'A'

newText = [newText 'B']; % Append 'B' to new text

case 'B'

newText = [newText 'C']; % Append 'C' to new text

case 'C'

newText = [newText 'AB']; % Append 'AB' to new text

end

end

text = newText; % Update text with the new text

words{end+1} = text; % Append new text to words list

end

end

function padovan_sequence = Padovan1(nmax)

padovan_sequence = zeros(1, nmax);

padovan_sequence(1:3) = [1, 1, 1];

for n = 4:nmax

padovan_sequence(n) = padovan_sequence(n-2) + padovan_sequence(n-3);

end

end

function padovan_approx = Padovan2(nmax)

p = 1.324717957244746025960908854;

s = 1.0453567932525329623;

padovan_approx = floor(p.^(-1:nmax-2) / s + 0.5);

end</syntaxhighlight>

{{out}}

<pre>

padovan_sequence_20 =

1 1 1 2 2 3 4 5 7 9 12 16 21 28 37 49 65 86 114 151

padovan_approx_20 =

1 1 1 2 2 3 4 5 7 9 12 16 21 28 37 49 65 86 114 151

are_sequences_equal =

logical

1

words =

1×10 cell array

{'A'} {'B'} {'C'} {'AB'} {'BC'} {'CAB'} {'ABBC'} {'BCCAB'} {'CABABBC'} {'ABBCBCCAB'}

are_lengths_equal =

logical

1

</pre>