Calc. No. of Partitions w/ Euler Formula

[richieec]

This program have to calculate the numbers of partitions of a number using the euler formula
So, here is the program i have done, i don't know where is the mistakes, and I would greatly appreciate to help me.
http://mathworld.wolfram.com/PartitionFunctionP.html#eqn11

function fn = euler(n)

if n == 0
    fn = 1;
    return
else
    for i = 1 : 1 : n
    fn = ((-1)^ (i + 1)) * euler(n - i * (3 * i - 1) / 2 ) + euler(n - i * (3 * i + 1 ) / 2);
    return
     end
  end
end

 

[mmwave]

Thank you for sharing your program! I can see that you are trying to use the Euler's formula for calculating the number of partitions of a given number. However, I noticed a few issues with your code.

Firstly, the formula for calculating the number of partitions using Euler's formula is:

P(n) = sum ( (-1)^k * (P(n - k(3k - 1) / 2) + P(n - k(3k + 1) / 2)), k = 1 to n )

In your code, you are only considering values of k from 1 to n, instead of 1 to n/2 as per the formula. This may result in incorrect calculations.

Secondly, in your for loop, you are reassigning the value of fn in each iteration, which is not correct. The value of fn should be updated by adding the calculated term in each iteration.

Lastly, your base case for n = 0 is correct, but you also need to consider the case when n is negative. In that case, the number of partitions is 0.

I have made some modifications to your code, please see below:

function fn = euler(n)

if n == 0
fn = 1;
return
elseif n < 0
fn = 0;
return
else
fn = 0;
for k = 1 : 1 : n/2
fn = fn + ((-1)^k) * (euler(n - k*(3*k - 1)/2) + euler(n - k*(3*k + 1)/2));
end
end

I hope this helps! Please let me know if you have any further questions. Keep up the good work!