How many rectangles a matrix can fit?

count_rectangles_inside_matrix.php

<?php

/**
 * Counts all rectangles inside matrix by loop.
 *
 * For 3x3:
 *  *_*_*   // 1x1 = 4
 *  *_*_*   // 1x2 = 2
 *  * * *   // 2x1 = 2
 *          // 2x2 = 1
 *
 * @param int $n
 * @param int $m
 * @return int
 */
function countRectInsideMatrix(int $n, int $m): int
{
    $w = $n;
    $count = 0;
    while (--$w > 0) {
        $h = $m;
        while (--$h > 0) {
            for ($i = 1; $i <= $n - $w; $i++) {
                for ($j = 1; $j <= $m - $h; $j++) {
                    if ($i + $w <= $n && $j + $h <= $m) {
                        $count++;
                    }
                }
            }
        }
    }

    return $count;
}

$i = 1;
do {
    printf("%dx%d = %d\n", $i, $i, countRectInsideMatrix($i, $i));
    printf("%dx%d = %d\n", $i + 1, $i, countRectInsideMatrix($i + 1, $i));
    printf("%dx%d = %d\n", $i, $i + 1, countRectInsideMatrix($i, $i + 1));
} while ($i++ < 10);

// 1x1 = 0
// 2x1 = 0
// 1x2 = 0
// 2x2 = 1
// 3x2 = 3
// 2x3 = 3
// 3x3 = 9
// 4x3 = 18
// 3x4 = 18
// 4x4 = 36
// 5x4 = 60
// 4x5 = 60
// 5x5 = 100
// 6x5 = 150
// 5x6 = 150
// 6x6 = 225
// 7x6 = 315
// 6x7 = 315
// 7x7 = 441
// 8x7 = 588
// 7x8 = 588
// 8x8 = 784
// 9x8 = 1008
// 8x9 = 1008
// 9x9 = 1296
// 10x9 = 1620
// 9x10 = 1620
// 10x10 = 2025
// 11x10 = 2475
// 10x11 = 2475