Another Family of Fibonacci-like Sequences

Peter R.J. Asveld

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    Abstract

    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.
    Original languageEnglish
    Pages (from-to)361-364
    Number of pages4
    JournalThe Fibonacci Quarterly
    Volume25
    Issue number4
    Publication statusPublished - 1987

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    Keywords

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

    Cite this

    Asveld, P. R. J. (1987). Another Family of Fibonacci-like Sequences. The Fibonacci Quarterly, 25(4), 361-364.
    Asveld, Peter R.J. / Another Family of Fibonacci-like Sequences. In: The Fibonacci Quarterly. 1987 ; Vol. 25, No. 4. pp. 361-364.
    @article{f17d64cffd8a43f2a4968a3072d9a632,
    title = "Another Family of Fibonacci-like Sequences",
    abstract = "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.",
    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",

    }

    Asveld, PRJ 1987, 'Another Family of Fibonacci-like Sequences', The Fibonacci Quarterly, vol. 25, no. 4, pp. 361-364.

    Another Family of Fibonacci-like Sequences. / Asveld, Peter R.J.

    In: The Fibonacci Quarterly, Vol. 25, No. 4, 1987, p. 361-364.

    Research output: Contribution to journalArticleAcademicpeer-review

    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

    VL - 25

    SP - 361

    EP - 364

    JO - The Fibonacci Quarterly

    JF - The Fibonacci Quarterly

    SN - 0015-0517

    IS - 4

    ER -