Generalizations of Sequences of Lucas and Bell

A. G. Shannon and A. F. Horadam

A chapter in Applications of Fibonacci Numbers, 1990, pp 299-309 from Springer

Abstract: Abstract Lucas defined second order “primordial” and “fundamental” recurring sequences and Bell defined third order “basic” recurring sequences. This paper defines arbitrary order generalizations of these sequences and establishes some inter-relationships amongst them. Specific examples of second and third order cases are given to illustrate the principal results. The relationship of the generalization to an extension of Pascal’s triangle is noted, and an application to the spread of infectious diseases is outlined.

Keywords: Recurrence Relation; Fibonacci Sequence; Initial Term; Exponential Generate Function; Linear Recurrence Relation (search for similar items in EconPapers)
Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-1910-5_33

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DOI: 10.1007/978-94-009-1910-5_33

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