Finite O-sequences of multiplicity d are counted up to d=1100 via a new algorithm, with sub-Fibonacci behavior proven for those ending above 1, Stanley-Zanello bounds calibrated empirically, and Roberts' 1992 question resolved negatively.
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Counting finite O-sequences: sub-Fibonacci behaviour and growth estimates
Finite O-sequences of multiplicity d are counted up to d=1100 via a new algorithm, with sub-Fibonacci behavior proven for those ending above 1, Stanley-Zanello bounds calibrated empirically, and Roberts' 1992 question resolved negatively.