Generate every sequence of K integers adding to N in any order, allowing for repeats

number_sequences.js

function generateSequences(n, k) {
	var sequences = [];

	function getSequences(n, k, sequence) {
		// calculate the highest possible value of a number, such that it leaves at least enough left over to fill the rest with 1s
		var upper = n - k + 1;

		for (var c = 1; c <= upper; c += 1) {
			var sub_sequence = sequence.slice(0);
			sub_sequence.push(c);

			// how many slots remain and how much remaining value do we have?
			var remaining_slots = k - 1;
			var remaining_value = n - c;

			if (remaining_slots == 1) {
				sub_sequence.push(remaining_value);
				sequences.push(sub_sequence.slice(0));
			} else {
				getSequences(n - c, k - 1, sub_sequence);
			}		
		}
	}
	getSequences(n, k, []);
	return sequences;
}

p = generateSequences(33, 4);

console.log(p);