I have some exercises which require knowing the number of partitions of particular numbers, so I used some python code which I found on internet to compute the values of the partition function for the values I want.
But I noticed that $p(10)=p(12)=57$ and $p(11)=51$ where $p$ is the partition function - this what the program gave me!
Before that, I guessed that the partition function is increasing, but the calculations by the code showed that it's not.
So, is my guess right and the code has an error, or is my guess wrong?
It's definitely increasing; given any partition of $n$, $$n=a_1+a_2+a_3+\cdots+a_k,$$ we have a corresponding partition of $n+1$, namely $$n+1=a_1+a_2+a_3+\cdots+a_k+1$$ so that there are at least as many partitions of $n+1$ are there are of $n$.
According to OEIS A000041, the first few values of the partition function are $$\begin{array}{r|r} n & a(n)\\\hline \tt 0 &\tt 1\\ \tt 1 &\tt 1\\ \tt 2 &\tt 2\\ \tt 3 &\tt 3\\ \tt 4 &\tt 5\\ \tt 5 &\tt 7\\ \tt 6 &\tt 11\\ \tt 7 &\tt 15\\ \tt 8 &\tt 22\\ \tt 9 &\tt 30\\ \tt 10 &\tt 42\\ \tt 11 &\tt 56\\ \tt 12 &\tt 77 \end{array}$$ so your program has a bug.