Another Family of Fibonacci-like Sequences

Peter R.J. Asveld

Another Family of Fibonacci-like Sequences

Peter R.J. Asveld

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Abstract

We consider the family of difference equations H_n = H{_n-1} + H{_n-2} + $\sum_{j=0}^k$ γ_jn{^(j)} with H₀ = H₁ = 1, n^(j)= n(n-1)(n-2)...(n-j+1) for j≥1 and n⁽⁰⁾ = 1. We express H_n in terms of the Fibonacci numbers and in the parameters γ1, . . . ,γk.

Original language	English
Pages (from-to)	361-364
Number of pages	4
Journal	The Fibonacci Quarterly
Volume	25
Issue number	4
Publication status	Published - 1987

Keywords

HMI-SLT: Speech and Language Technology
MSC-11B39

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@article{f17d64cffd8a43f2a4968a3072d9a632,

title = "Another Family of Fibonacci-like Sequences",

abstract = "We consider the family of difference equations Hn = H\{n-1\} + H\{n-2\} + \$\textbackslash{}sum\_\{j=0\}\textasciicircum{}k\$ γjn\{(j)\} with H0 = H1 = 1, n(j) = n(n-1)(n-2)...(n-j+1) for j≥1 and n(0) = 1. We express Hn in terms of the Fibonacci numbers and in the parameters γ1, . . . ,γk.",

keywords = "HMI-SLT: Speech and Language Technology, MSC-11B39",

author = "Asveld, \{Peter R.J.\}",

note = "In the typesetting process an error occurred: op page 362 in line +2, the second summation should be from \$i=0\$ to \$k\$ and the third one from \$l=0\$ to \$i\$; cf. http://eprints.eemcs.utwente.nl/5256 page 2, line +6.",

year = "1987",

language = "English",

volume = "25",

pages = "361--364",

journal = "The Fibonacci Quarterly",

issn = "0015-0517",

publisher = "Fibonacci Association",

number = "4",

}

TY - JOUR

T1 - Another Family of Fibonacci-like Sequences

AU - Asveld, Peter R.J.

N1 - In the typesetting process an error occurred: op page 362 in line +2, the second summation should be from $i=0$ to $k$ and the third one from $l=0$ to $i$; cf. http://eprints.eemcs.utwente.nl/5256 page 2, line +6.

PY - 1987

Y1 - 1987

N2 - We consider the family of difference equations Hn = H{n-1} + H{n-2} + $\sum_{j=0}^k$ γjn{(j)} with H0 = H1 = 1, n(j) = n(n-1)(n-2)...(n-j+1) for j≥1 and n(0) = 1. We express Hn in terms of the Fibonacci numbers and in the parameters γ1, . . . ,γk.

AB - We consider the family of difference equations Hn = H{n-1} + H{n-2} + $\sum_{j=0}^k$ γjn{(j)} with H0 = H1 = 1, n(j) = n(n-1)(n-2)...(n-j+1) for j≥1 and n(0) = 1. We express Hn in terms of the Fibonacci numbers and in the parameters γ1, . . . ,γk.

KW - HMI-SLT: Speech and Language Technology

KW - MSC-11B39

M3 - Article

SN - 0015-0517

VL - 25

SP - 361

EP - 364

JO - The Fibonacci Quarterly

JF - The Fibonacci Quarterly

IS - 4

ER -

Another Family of Fibonacci-like Sequences

Abstract

Keywords

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