Tournament bracket customized algorithm

I'm in the making of a tournament for archery but i'm stuck because they want a specific match-matching for players. There is the usual 1-32,2-31,3-30 etc but the way they want the tree is a specific one.

For now i'm producing the array with this

$players = range(1, $range);
$count = count($players);
for ($i = 0; $i < log($count / 2, 2); $i++) {
    echo $i;
    echo '<br>';
    print "<pre>";
    print_r($players);
    print "</pre>";
    $out = array();
    foreach ($players as $player) {
        $splice = pow(2, $i);

        $out = array_merge($out, array_splice($players, 0, $splice));

        $out = array_merge($out, array_splice($players, -$splice));
    }

    $players = $out;
}

With an output of

Array
(
    [0] => 1
    [1] => 16
    [2] => 8
    [3] => 9
    [4] => 4
    [5] => 13
    [6] => 5
    [7] => 12
    [8] => 2
    [9] => 15
    [10] => 7
    [11] => 10
    [12] => 3
    [13] => 14
    [14] => 6
    [15] => 11
)

Everything works great except they want the tree like this

Array
(
    [0] => 1
    [1] => 16
    [2] => 9
    [3] => 8
    [4] => 5
    [5] => 12
    [6] => 13
    [7] => 4
    [8] => 3
    [9] => 14
    [10] => 11
    [11] => 6
    [12] => 7
    [13] => 10
    [14] => 15
    [15] => 2
)

You will notice some differences between those to. For example 2-15 match is at position 8 and 9 of the array while in the second one it's at 14-15.

I've been busting my head to find an algorithm for this but i'm stuck.

Thanks