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Properties of Cordonnier, Perrin and Van der Laan numbers. (English) Zbl 1149.11300

Summary: This paper aims to explore some properties of certain third-order linear sequences which have some properties analogous to the better-known second-order sequences of Fibonacci and Lucas. Historical background issues are outlined. These, together with the number and combinatorial theoretical results, provide plenty of pedagogical opportunities for further development.

MSC:

11B37 Recurrences
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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References:

[1] Lucas E, A. F. Congrès du Clerment-Ferrand pp 61– (1876)
[2] DOI: 10.1038/scientificamerican0296-92
[3] Perrin R, L’Intermédiaire des Math 6 pp 76– (1899)
[4] DOI: 10.1215/S0012-7094-71-03895-6 · Zbl 0226.05008
[5] de Weger BMM, Publications Matemàtiques 41 pp 631– (1997) · Zbl 0899.11004
[6] Feinberg M, Fibonacci Quarterly 1 pp 71– (1963)
[7] Fairgrieve S, Fibonacci Quarterly 43 pp 137– (2005)
[8] DOI: 10.1142/9789812776839
[9] Benjamin AT, Proofs That Really Count: The Art of Combinatorial Proof (2003) · Zbl 1044.11001
[10] Shannon AG, Fibonacci Quarterly 40 pp 405– (2002)
[11] DOI: 10.1080/00207390210212 · Zbl 1006.26009
[12] DOI: 10.2307/2324364 · Zbl 0812.11021
[13] DOI: 10.1080/0020739031000148886 · Zbl 02354856
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