Polynomial Galileo sequences are exactly a_n = C (n^d - (n-1)^d); every positive Galileo sequence has a binary-tree representation, and monotone integer ones obey power-law growth bounds with a full characterization of their continuous analogs.
May.Galileo sequences, a good dangling problem
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Structure and Growth of Galileo Sequences
Polynomial Galileo sequences are exactly a_n = C (n^d - (n-1)^d); every positive Galileo sequence has a binary-tree representation, and monotone integer ones obey power-law growth bounds with a full characterization of their continuous analogs.