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The generalized order-k Narayana's cows numbers

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Veröffentlicht/Copyright: 3. November 2016
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 66 Heft 4

Abstract

Narayana’s cows problem is a problem similar to the Fibonacci’s rabbit problem. We define the numbers which are the solutions of this problem as Narayana’s cows numbers. Narayana’s cows sequence satisfies the third order recurrence relation Nr = Nr−1+Nr−3 with initial condition N0 = N1 = N2 = 1. In this paper, we define a new recurrence which is called generalized order-k Narayana’s cows sequence and by using this generalization and some matrix properties, we give some identities related to the Narayana’s cows numbers.

MSC 2010: Primary 11B83
Keywords: generalized Narayana’s cows number; generating function; Binet formula; matrix method

(Communicated by Stanislav Jakubec)

References

1 Er, M. C.: Sums of Fibonacci numbers by matrix methods, Fibonacci Quart. 22 (1984), 204—207.10.1080/00150517.1984.12429883Suche in Google Scholar

2 Kalman, D.: Generalized Fibonacci numbers by matrix methods, Fibonacci Quart. 20 (1982), 73—76.10.1080/00150517.1982.12430034Suche in Google Scholar

3 Kilic, E.—Tasci, D.: The generalized Binet formula, representation and sums of the generalized order-k Pell numbers, Taiwanese J. Math. 10 (2006), 1661—1670.10.11650/twjm/1500404581Suche in Google Scholar

4 Sloane, N. J. A.: The Online Encyclopedia of Integer Sequences, Sequence A000930 (Narayana’s Cows Sequence). http://oeis.org/A000930Suche in Google Scholar

5 Tasci, D.—Kilic, E.: On the order-k generalized Lucas numbers, Appl. Math. Comput. 155 (2004), 637—641, DOI: 10.1016/S0096-3003(03)00804-X.10.1016/S0096-3003(03)00804-XSuche in Google Scholar

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Received: 2012-12-6
Accepted: 2014-2-19
Published Online: 2016-11-3
Published in Print: 2016-8-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0181
Schlagwörter für diesen Artikel
generalized Narayana’s cows number; generating function; Binet formula; matrix method

Artikel in diesem Heft

  1. Research Article
  2. Effect algebras with a full set of states
  3. Research Article
  4. An approach to orthomodular lattices via lattices with an antitone involution
  5. Research Article
  6. On properties of the free BCI-algebra with one generator
  7. Research Article
  8. The generalized order-k Narayana's cows numbers
  9. Research Article
  10. The irrationality of infinite series of a special kind
  11. Research Article
  12. On skew-commuting mappings in semiprime rings
  13. Research Article
  14. On the subordination and superordination of strongly starlike functions
  15. Research Article
  16. On a subclass of analytic functions involving Sălăgean integral operator
  17. Research Article
  18. Uniqueness of meromorphic functions sharing a value or small function
  19. Research Article
  20. A new inclusion for Bavrin's families of holomorphic functions in n-circular domains
  21. Research Article
  22. Oscillation of nonlinear fourth order mixed neutral differential equations
  23. Research Article
  24. Oscillation results for third order nonlinear mixed neutral differential equations
  25. Research Article
  26. Homoclinic solutions for second order Hamiltonian systems with general potentials
  27. Research Article
  28. A class of fractional impulsive functional differential equations with nonlocal conditions
  29. Research Article
  30. The weighted reverse poincaré type inequality for the difference of two parabolic subsolutions
  31. Research Article
  32. On the well posed solutions for nonlinear second order neutral difference equations
  33. Research Article
  34. Some approximation results for operators of Szász-Mirakjan-Durrmeyer type
  35. Research Article
  36. On the geometry of conditional expectations treated as projections on the L2-space
  37. Research Article
  38. Spectral problems of nonself-adjoint singular discrete Sturm-Liouville operators
  39. Research Article
  40. A necessary condition for the Smith equivalence of G-modules and its sufficiency
  41. Research Article
  42. On the internal approach to differential equations. 1. The involutiveness and standard basis
  43. Research Article
  44. Law of inertia for the factorization of cubic polynomials — the case of discriminants divisible by three
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