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Triangular numbers and generalized fibonacci polynomial

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Published/Copyright: December 4, 2022
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 72 Issue 6

Abstract

In the present paper, we study triangular numbers. We focus on the linear homogeneous recurrence relation of degree 3 with constant coefficients for triangular numbers. Then we deal with the relationship between generalized Fibonacci polynomials and triangular numbers. We show that different properties of triangular numbers can be obtained by using this relationship. Finally, we examine the properties of the sequence A052529 that has strong relationships with triangular numbers.

Keywords: Alternating triangular numbers; triangular numbers; generalized Fibonacci polynomials
MSC 2010: Primary 11B39; 11B37; Secondary 15A15

  1. (Communicated by István Gaál)

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Received: 2021-04-16
Accepted: 2021-11-13
Published Online: 2022-12-04
Published in Print: 2022-12-16

© 2022 Mathematical Institute Slovak Academy of Sciences

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  7. A general matrix series inversion pair and associated polynomials
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https://doi.org/10.1515/ms-2022-0099
Keywords for this article
Alternating triangular numbers; triangular numbers; generalized Fibonacci polynomials

Articles in the same Issue

  1. Prof. RNDr. Július korbaš, CSC. passed away
  2. Kalmbach measurability In d0-algebras
  3. Quantifiers on L-algebras
  4. Ideals of functions with compact support in the integer-valued case
  5. An algebraic study of the logic S5’(BL)
  6. Triangular numbers and generalized fibonacci polynomial
  7. A general matrix series inversion pair and associated polynomials
  8. Quantum ostrowski type inequalities for pre-invex functions
  9. Hermite-Hadamard type inequalities for interval-valued fractional integrals with respect to another function
  10. Approximating families for lattice outer measures on unsharp quantum logics
  11. On a generalized Lamé-Navier system in ℝ3
  12. Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions
  13. On some classical properties of normed spaces via generalized vector valued almost convergence
  14. Fan-Hemicontinuity for the gradient of the norm in Hilbert space
  15. Solvability of mixed problems for heat equations with two nonlocal conditions
  16. The global harnack estimates for a nonlinear heat equation with potential under finsler-geometric flow
  17. A note on set-star-K-Menger spaces
  18. A bivariate extension of the Omega distribution for two-dimensional proportional data
  19. Bernstein polynomials based iterative method for solving fractional integral equations
  20. The symmetric 4-Player gambler’s problem with unequal initial stakes
  21. Enveloping action: Convergence spaces
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