Bounded Part Distribution Calculator

This script computes and analyzes bounded part distributions for a range of integers. Specifically, it generates all partitions of integers, where the size of each part is bounded by a specified maximum value. The program then counts how many partitions contain 1's, 2's, and 3's, and summarizes this distribution for each integer within a given range.

Features

• Partition Calculation: Generates all partitions of an integer k where each part size is bounded by max_part.
• Range-based Analysis: Computes the distribution of partitions for all integers within a specified range (from start_k to end_k).
• Customizable Parameters: The maximum part size and the integer range can be customized for your analysis.

Requirements

• Python 3.x
• sympy library

To install the necessary libraries, you can use pip:

pip install sympy