Journal of Integer Sequences, Vol. 26 (2023), Article 23.7.5

Sequences Derived from the Symmetric Powers of {1, 2, ..., k}

Po-Yi Huang and Wen-Fong Ke
Department of Mathematics
National Cheng Kung University
Tainan 701


For a fixed integer k, we define a sequence Ak = (ak(n))n ≥ 0 and a corresponding sparse subsequence Sk using the cardinality of the n-th symmetric power of the set {1, 2, ..., k}. For k ∈ {2,...,8}, we find recursive formulas for Sk, and show that the values ak(0), ak(1), and ak(3) are sufficient for constructing Ak.

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(Concerned with sequences A000012 A001316 A048883 A253064.)

Received June 19 2023; revised versions received June 25 2023; August 1 2023; August 4 2023. Published in Journal of Integer Sequences, August 5 2023.

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