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Journals / Turkish Journal of Mathematics / 2021 / Cilt: 45 - Sayı: 1

A new recursive formula arising from a determinantal expression for weighted Delannoy numbers

Muhammet Cihat DAĞLI
Pages
471–478
Publication Date
2022-11-01
DOI
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AI Summary & Key Takeaways

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

For the special case of our formula, we compute central weighted Delannoy number in terms of weighted Delannoy number.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we obtain a determinantal expression for weighted Delannoy numbers, from which we give a new recurrence relation for it.
📊
Key Findings & Data:In this paper, we obtain a determinantal expression for weighted Delannoy numbers, from which we give a new recurrence relation for it.
💡
Conclusion & Impact:For the special case of our formula, we compute central weighted Delannoy number in terms of weighted Delannoy number.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we obtain a determinantal expression for weighted Delannoy numbers, from which we give a new recurrence relation for it. For the special case of our formula, we compute central weighted Delannoy number in terms of weighted Delannoy number.

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Cite This Article

DAĞLI, M. C. (2022). A new recursive formula arising from a determinantal expression for weighted Delannoy numbers. Turkish Journal of Mathematics, Cilt: 45 - Sayı: 1, 471–478. https://ajindex.com/articles/607323

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References (15)

  1. Banderier C, Schwer S. Why Delannoy numbers? Journal of Statistical Planning and Inference 2005
  2. doi: 10.1016/j.jspi.2005.02.004 [2] Bourbaki N. Functions of a Real Variable, Elementary Theory. Translated from the 1976 French Original by Philip Spain. Elements of Mathematics (Berlin). Berlin, Germany: Springer, 2004. doi: 10.1007/978-3-642-59315-4 [3] Cahill ND, D’Errico JR, Narayan DA, Narayan JY. Fibonacci determinants. The College Mathematics Journal 2002
  3. 33 (3): 221-225. doi: 10.2307/1559033 [4] Caughman JS, Haithcock CR, Veerman JJP. A note on lattice chains and Delannoy numbers. Discrete Mathematics 2008
  4. 308 (12): 2623-2628. doi: 10.1016/j.disc.2007.05.017 [5] Dağlı MC. A new generalization of Delannoy numbers. Indian Journal of Pure and Applied Mathematics 2020
  5. 51 (4) 1729-1735. doi: 10.1007/s13226-020-0492-7 [6] Fray RD, Roselle DP. Weighted lattice paths. Pacific Journal of Mathematics 1971
  6. 37 (1): 85-96. [7] Fray RD, Roselle DP. On weighted lattice paths. Journal of Combinatorial Theory, Series A 1973
  7. 14 (1): 21-29. doi: 10.1016/0097-3165(73)90060-5 [8] Guo VJW. Proof of Sun’s conjectures on integer-valued polynomials. Journal of Mathematical Analysis and Applications 2016
  8. doi: 10.1016/j.jmaa.2016.06.028 [9] İpek A, Arı K. On Hessenberg and pentadiagonal determinants related with Fibonacci and Fibonacci-like numbers. Applied Mathematics and Computation 2014
  9. doi: 10.1016/j.amc.2013.12.071 [10] Liu JC. A supercongruence involving Delannoy numbers and Schröder numbers. Journal of Number Theory 2016
  10. doi: 10.1016/j.jnt.2016.04.019 [11] Liu JC, Li L, Wang SD. Some congruences on Delannoy numbers and Schröder numbers. International Journal of Number Theory 2018
  11. doi: 10.1142/S1793042118501221 [12] Noble R. Asymptotics of the weighted Delannoy numbers. International Journal of Number Theory 2012
  12. 8 (1): 175-188. doi: 10.1142/S1793042112500108 [13] Qi F. Denying a short proof of a determinantal formula for generalized Fibonacci polynomials. Journal of Mathematical Analysis 2020
  13. 11 (1): 52-57. [14] Qi F. Derivatives of tangent function and tangent numbers. Applied Mathematics and Computation 2015
  14. doi: 10.1016/j.amc.2015.06.123 [15] Qi F. A determinantal expression and a recursive relation of the Delannoy numbers. Acta Universitatis Sapientiae Mathematica 2021
  15. 13 (1) (in press). [16] Qi F, Cernanova V, Semenov YS. Some tridiagonal determinants related to centra