The size of the h-fold sumset is the binomial maximum until h reaches a lattice minimum, then drops by a second binomial term until the next minimum, producing triangular-number differences for four-element sets.
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On Nathanson's Triangular Number Phenomenon
The size of the h-fold sumset is the binomial maximum until h reaches a lattice minimum, then drops by a second binomial term until the next minimum, producing triangular-number differences for four-element sets.