The Rambam in his Pirush Hamishnayos, Introduction to Perek Chailek (10th or 11th chapter in Sanhedrin), says explicitly that Moshiach will have at least one son, who will become melech after he passes away. That son will have a son who will become melech after the son, so that Malchus HaMoshiach will last at least three generations.
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