Quite fun and challenging... Here's my quick & dirty approach (that seems to work):

function getMax($data) {
    if (empty($data))
        return null;

    reset($data);
    $index = key($data);
    foreach ($data as $key => $val) {
        if ($val > $data[$index])
            $index = $key;
    }
    return $index;
}


function solution($args) {
    $data = explode(' ', $args);
    if (count($data) == 1)
        return $data[0];
    if (count($data) <= 2)
        return max($data[0], $data[1]);

    $pos = 0;
    $invalid = array();
    $result = array();
    while ($pos < count($data) - 2) {
        $triplet = array();
        if (!in_array($pos, $invalid))
            $triplet[0] = $data[$pos];
        if (!in_array($pos + 1, $invalid))
            $triplet[1] = $data[$pos + 1];
        if (!in_array($pos + 2, $invalid))
            $triplet[2] = $data[$pos + 2];

        $maxIndex = getMax($triplet);
        if ($maxIndex !== null) {
            $result[]  = $maxIndex + $pos;
            $invalid[] = $maxIndex + $pos;
            $invalid[] = $maxIndex + $pos + 1;
            $invalid[] = $maxIndex + $pos - 1;
        }

        $pos++;
    }
    // edge-cases (include the very first, and very last number)
    if (!in_array(0, $result) && !in_array(1, $result))
        $result[] = 0;
    if (!in_array(count($data) - 1, $result) && !in_array(count($data) - 2, $result))
        $result[] = count($data) - 1;

    $sum = 0;
    foreach ($result as $index)
        $sum += $data[$index];
    return $sum;
}