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arXiv · 2205.03845

A System of Four simultaneous Recursions: Generalization of the Ledin-Shannon-Ollerton Identity

Russell Jay Hendel
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Abstract

This paper further generalizes a recent result of Shannon and Ollerton who resurrected an old identity due to Ledin. This paper generalizes the Ledin-Shannon-Ollerton result to all the metallic sequences. The results give closed formulas for the sum of products of powers of the first $n$ integers with the first $n$ members of the metallic sequence. Three key innovations of this paper are i) reducing the proof of the generalization to the solution of a system of 4 simultaneous recursions; ii) use of the shift operation to prove equality of polynomials; and iii) new OEIS sequences arising from the coefficients of the four polynomial families satisfying the 4 simultaneous recursions.

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Russell Jay Hendel. 2022-05-08. A System of Four simultaneous Recursions: Generalization of the Ledin-Shannon-Ollerton Identity. https://arxiv.org/abs/2205.03845

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