Get all the combinations a number can be split into - php

Question

I have a fixed number (5) and a fixed length (2):
I want to find all the combinations that can sum 50 (this can vary of course).
For example, for 50, and a length of 2, I want to get:
[[1, 49], [2, 48], [3, 47], [4, 46], ...],
For 50 and a length of 4, I want to get:
[[1, 1, 1, 47], [1, 1, 2, 46], [1, 1, 3, 45], [1, 1, 4, 44], ...],
I have no clue how to do this, or whether there's a name in mathematics for this.
This is what I have (doesn't have to use generators):
function getCombinations(array $numbers, int $sum, int $setLength) : \Generator {
$numbersLowestFirst = $numbers;
asort($numbersLowestFirst);
$lowestNumber = 0;
foreach ($numbersLowestFirst as $number) {
// array might be associative and we want to preserve the keys
$lowestNumber = $number;
break;
}
$remainingAmount = $sum - $lowestNumber;
$remainingNumberofItems = $setLength - 1;
$possibleItemCombinations = array_pad([$remainingAmount], $remainingNumberofItems, $lowestNumber);
}

Answer 1

I first made it using JS then translated to PHP. See below for a JS demonstration. The idea is as #Barmar said in comments.
Note: There will be duplicates. If you care for that, you should sort each "triplet" and look for duplications. See JS solution for that below.
function getCombinations($sum, $n)
{
if ($n == 1) {
return [[$sum]];
}
$arr = [];
for ($i = 0; $i <= $sum / 2; $i++) {
$combos = getCombinations($sum - $i, $n - 1);
foreach ($combos as $combo) {
$combo[] = $i;
$arr[] = $combo;
}
}
return ($arr);
}
JS style, it's the same idea only more comfortable to test on browser.
function getCombinations(sum, n) {
if (n == 1) return [[sum]];
var arr = []
for (var i = 0; i <= sum / 2; i++) {
var combos = getCombinations(sum - i, n - 1)
combos.forEach(combo => {
arr.push([i, ...combo]);
})
}
// removing duplicates
arr = Object.values(arr.reduce(function(agg, triplet) {
triplet = triplet.sort();
agg["" + triplet] = triplet;
return agg;
}, {}))
return arr;
}
console.log(getCombinations(5, 3))