Some formulae for the fibonacci numbers

Brian Curtin; Ena Salter; David Stone

Some formulae for the fibonacci numbers

Brian Curtin, Ena Salter, David Stone

Emeriti, Retired, & In Memoriam (COSM)

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

2 Scopus citations

Abstract

Using elementary methods, we derive formulae for the shifted summations Σ_j=0^d-1 F_n+j F_m+j, Σ_j=0^d-1 L_n+j L_m+j and Σ_j=0^d-1 F_n+j L_m+j and the shifted convolutions Σ_j=0^d-1 F_n+j F _d-m-j, Σ_j=0^d-1 L_n+j L _d-m-j, and Σ_j=0^d-1 F_n+j L _d-m-j for positive integers d and arbitrary integers n and m.

Original language	English
Pages (from-to)	171-180
Number of pages	10
Journal	Fibonacci Quarterly
Volume	45
Issue number	2
State	Published - May 2007

Cite this

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title = "Some formulae for the fibonacci numbers",

abstract = "Using elementary methods, we derive formulae for the shifted summations Σj=0d-1 Fn+j Fm+j, Σj=0d-1 Ln+j Lm+j and Σj=0d-1 Fn+j Lm+j and the shifted convolutions Σj=0d-1 Fn+j F d-m-j, Σj=0d-1 Ln+j L d-m-j, and Σj=0d-1 Fn+j L d-m-j for positive integers d and arbitrary integers n and m.",

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AU - Salter, Ena

AU - Stone, David

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N2 - Using elementary methods, we derive formulae for the shifted summations Σj=0d-1 Fn+j Fm+j, Σj=0d-1 Ln+j Lm+j and Σj=0d-1 Fn+j Lm+j and the shifted convolutions Σj=0d-1 Fn+j F d-m-j, Σj=0d-1 Ln+j L d-m-j, and Σj=0d-1 Fn+j L d-m-j for positive integers d and arbitrary integers n and m.

AB - Using elementary methods, we derive formulae for the shifted summations Σj=0d-1 Fn+j Fm+j, Σj=0d-1 Ln+j Lm+j and Σj=0d-1 Fn+j Lm+j and the shifted convolutions Σj=0d-1 Fn+j F d-m-j, Σj=0d-1 Ln+j L d-m-j, and Σj=0d-1 Fn+j L d-m-j for positive integers d and arbitrary integers n and m.

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SP - 171

EP - 180

JO - Fibonacci Quarterly

JF - Fibonacci Quarterly

IS - 2

ER -

Some formulae for the fibonacci numbers

Abstract

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