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math.CO2024
Partitions in which every term but the smallest one is consecutive
Rajat Gupta, Noah Lebowitz-Lockard
In this article, we introduce the notion of almost consecutive partitions. A partition is almost consecutive if every term is consecutive, with the possible exception of the smalle…
math.CO2023
Non-standard binary representations and the Stern sequence
Katie Anders, Madeline Locus Dawsey, Rajat Gupta +1
We show that the number of short binary signed-digit representations of an integer is equal to the -th term in the Stern sequence. Various proofs are provided, including dir…