A note on Ledin’s summation problem

Anthony G. Shannon; Richard L. Ollerton

A note on Ledin’s summation problem

Anthony G. Shannon, Richard L. Ollerton

Computing, Mathematics and Engineering

University of New South Wales

Research output: Contribution to journal › Article › peer-review

Abstract

This paper takes a historical view of some long-standing issues associated with polynomials developed from sums of Fibonacci numbers in which the latter have powers of integers as coefficients. The sequences of coefficients of these polynomials are arrayed in matrices with links to The On-Line Encyclopedia of Integer Sequences. Problems for further study are conjectured, including inhomogeneous gibonacci difference equations.

Original language	English
Pages (from-to)	47-56
Number of pages	10
Journal	The Fibonacci Quarterly
Volume	59
Issue number	1
Publication status	Published - Feb 2021

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title = "A note on Ledin{\textquoteright}s summation problem",

abstract = "This paper takes a historical view of some long-standing issues associated with polynomials developed from sums of Fibonacci numbers in which the latter have powers of integers as coefficients. The sequences of coefficients of these polynomials are arrayed in matrices with links to The On-Line Encyclopedia of Integer Sequences. Problems for further study are conjectured, including inhomogeneous gibonacci difference equations.",

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AB - This paper takes a historical view of some long-standing issues associated with polynomials developed from sums of Fibonacci numbers in which the latter have powers of integers as coefficients. The sequences of coefficients of these polynomials are arrayed in matrices with links to The On-Line Encyclopedia of Integer Sequences. Problems for further study are conjectured, including inhomogeneous gibonacci difference equations.

KW - Fibonacci sequence

KW - Summation

KW - Recurrence

KW - Powers of integers

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UR - https://www.fq.math.ca/

M3 - Article

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VL - 59

SP - 47

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JO - The Fibonacci Quarterly

JF - The Fibonacci Quarterly

IS - 1

ER -

A note on Ledin’s summation problem

Abstract

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