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Journals / Gazi University Journal of Science / 2021 / Volume: 34 Issue: 4

Some Properties of a Third Order Partial Recurrence Relation

Anthony G. Shannon(Warrane College, the University of New South Wales)0000-0003-0116-0666
Ömür Deveci(KAFKAS UNIVERSITY)0000-0001-5870-5298
Pages
—
Publication Date
2021-12-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

It does this with a partial recurrence relation which is related to the original third order recurrence relation, and raises a related conjecture.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper explores a connection between third order recursive sequences and generalized continued fractions by analogy with second order recursive sequences and ordinary two-dimensional continued fractions.
📊
Key Findings & Data:This paper explores a connection between third order recursive sequences and generalized continued fractions by analogy with second order recursive sequences and ordinary two-dimensional continued fractions.
💡
Conclusion & Impact:It does this with a partial recurrence relation which is related to the original third order recurrence relation, and raises a related conjecture.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fibonacci numbers · Tribonacci numbers · Partial quotients

Abstract

This paper explores a connection between third order recursive sequences and generalized continued fractions by analogy with second order recursive sequences and ordinary two-dimensional continued fractions. It does this with a partial recurrence relation which is related to the original third order recurrence relation, and raises a related conjecture.

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Cite This Article

Shannon, A. G., Deveci, Ö. (2021). Some Properties of a Third Order Partial Recurrence Relation. Gazi University Journal of Science, Volume: 34 Issue: 4. https://doi.org/10.35378/gujs.770440

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References (16)

  1. Horadam, A.F., “Basic properties of a certain generalized sequence of numbers”, The Fibonacci Quarterly, 3: 161-176, (1965).
  2. Deveci, O. and Shannon, A.G., “Pell-Padovan-circulant sequences and their applications”, Notes on Number Theory and Discrete Mathematics, 23 (3): 100-114, (2017).
  3. Sloane, N.J.A., “The On-Line Encyclopedia of Integer Sequences”, http://oeis.org, (1964).
  4. Hildebrand, F.B., Introduction to Numerical Analysis, McGraw-Hill, New York, p.461, (1956).
  5. Feinberg, M., “New Slants”, The Fibonacci Quarterly, 2: 223-227, (1964).
  6. Jarden, D., Recurring Sequences, Jerusalem: Riveon Lematika, p.114, (1966).
  7. Shannon, A.G., Anderson, P.G. and Horadam, A.F., “Properties of Cordonnier, Perrin and Van der Laan numbers”, International Journal of Mathematical Education in Science and Technology, 37: 825-831, (2006).
  8. Shannon, A.G., Horadam, A.F. and Anderson, P.G., “The auxiliary equation associated with the Plastic number”, Notes on Number Theory and Discrete Mathematics, 12: 1-12, (2006).
  9. Shannon, A.G. and Wong, C.K., “Some Properties of Generalized Third Order Pell Numbers”, Congressus Numerantium, 201: 345-351, (2010).
  10. Gnanadoss, A.A., “Contracting Bernoulli’s iteration and recurrence relations”, The Mathematical Gazette, 44: 221-223, (1960).
  11. Anderson, P.G., Brown, T.C. and Shiue, P.J.-S., “A simple proof of a remarkable continued fraction identity”, Proceedings of the American Mathematical Society, 123:2005-2009, (1995).
  12. Anderson, P.G., “Notes and extensions for a remarkable continued fraction”, The Fibonacci Quarterly, 55: 9-14, (2017).
  13. Van der Cruyssen, P., “Linear difference equations and generalized continued fractions”, Computing, 22: 269-278, (1979).
  14. Szekeres, G., “Multidimensional Continued Fractions”, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae Sectio Mathematica, 13: 113–140, (1970).
  15. Van der Cruyssen. P., “A continued fraction algorithm”, Numerische Mathematik, 37: 149-156, ( 1981).
  16. Bernstein, L., The Jacobi-Perron Algorithm: Its Theory and Application (Lecture Notes in Mathematics 207), Berlin: Springer, Ch.2, (1971).