A function in PHP that takes an integer and returns all sequences of numbers that sum to it. For example, 3 => (1, 1, 1), (1, 2), (2, 1), (3)

sequencesThatSumToNumber.php

<?php 

/**
 * Returns an array containing all sequences of numbers that sum to $num,
 * e.g. sequencesThatSumToNumber(3) => array(array(1, 1, 1), array(1, 2), array(2, 1), array(3))
 *
 * @param int $num
 * @return array
 */
function sequencesThatSumToNumber($num) {
    $result = array(); // base case
    
    if ($num > 0) {
        // take one summand and add it to all sequences of the rest
        for ($i = 1; $i < $num; ++$i) {
            $subsequences = sequencesThatSumToNumber($num - $i);
            
            foreach ($subsequences as $sequence) {
                $result[] = array_merge(array($i), $sequence);
            }
        }
        
        // don't forget to add $num, since it sums to itself too
        $result[] = array($num);    
    }
    return $result;
}