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Number of Subsets of the Set [n] Including No Three Consecutive Odd Integers.

Year 2021, Issue: 28, 352 - 356, 30.11.2021
https://doi.org/10.31590/ejosat.999521

Abstract

For every natural number, let the sequence enumerate the number of subsets S of the set {1,2, . . . ,n } including no three consecutive odd integers. We give the generating function and the closed form formula of the sequence obtaining sixth order linear homogeneous recurrence relation with constant coefficients of the integer sequence. The sequence is associated with the Tribonacci sequence. The combinatorial representation of the sequence is obtained and limit of the ratios of consecutive terms of the sequence is found.

References

  • Bueno, A. C. F. (2015). A note on generalized Tribonacci sequence, Notes on Number Theory and Discrete Mathematics, 21, 67-69.
  • Feinberg, M. (1963). Fibonacci–Tribonacci, Fibonacci Quarterly, 1, 71–74.
  • Pethe, S. (1988). Some Identities for Tribonacci sequences, Fibonacci Q., 26, 144–151.
  • Ramirez, J. L. and Sirvent, V. F. (2014), Incomplete Tribonacci numbers and polynomials, Journal of Integer Sequences, 17 Article 14.4.2.
  • Shannon, A. (1977). Tribonacci numbers and Pascal’s pyramid, Fibonacci Q., 15, 268–275.
  • Spickerman, W. and Joyner, R. N. Binets’s formula for the Recursive sequence of Order K, Fibonacci Q., 22, 327–331.
  • Spickerman, W. (1982). Binet’s formula for the Tribonacci sequence, Fibonacci Q., 20, (118-120).
  • Wilf, H. S. (1990). Generatingfunctionology, Academic Press.
  • Yalavigi, C. C. (1972), Properties of Tribonacci numbers, Fibonacci Quarterly, 10 231–246.
  • Yilmaz, N. and Taskara, N. (2014). Tribonacci and Tribonacci-Lucas Numbers via the Determinants of Special Matrices, Appl. Math. Sci., 8(39), 1947–1955.

[n] Kümesinin Ardışık Üç Tam Sayı İçermeyen Alt Kümelerinin Sayısı

Year 2021, Issue: 28, 352 - 356, 30.11.2021
https://doi.org/10.31590/ejosat.999521

Abstract

Her doğal sayı için, {1,2, . . . ,n } kümesinin ardışık üç tek tam sayı içermeyen S alt kümelerinin sayısını veren tam sayı dizisini ele alalım . Dizinin altıncı dereceden sabit katsayılı lineer homojen rekürans bağıntısını elde ederek dizinin üreteç fonksiyonunu ve kapalı form formülünü verdik. Dizi Tribonacci sayı dizisi ile ilişkilendirildi. Dizinin kombinatoryal gösterimi elde edildi ve dizinin ardışık terimlerinin oranlarının limiti bulundu.

References

  • Bueno, A. C. F. (2015). A note on generalized Tribonacci sequence, Notes on Number Theory and Discrete Mathematics, 21, 67-69.
  • Feinberg, M. (1963). Fibonacci–Tribonacci, Fibonacci Quarterly, 1, 71–74.
  • Pethe, S. (1988). Some Identities for Tribonacci sequences, Fibonacci Q., 26, 144–151.
  • Ramirez, J. L. and Sirvent, V. F. (2014), Incomplete Tribonacci numbers and polynomials, Journal of Integer Sequences, 17 Article 14.4.2.
  • Shannon, A. (1977). Tribonacci numbers and Pascal’s pyramid, Fibonacci Q., 15, 268–275.
  • Spickerman, W. and Joyner, R. N. Binets’s formula for the Recursive sequence of Order K, Fibonacci Q., 22, 327–331.
  • Spickerman, W. (1982). Binet’s formula for the Tribonacci sequence, Fibonacci Q., 20, (118-120).
  • Wilf, H. S. (1990). Generatingfunctionology, Academic Press.
  • Yalavigi, C. C. (1972), Properties of Tribonacci numbers, Fibonacci Quarterly, 10 231–246.
  • Yilmaz, N. and Taskara, N. (2014). Tribonacci and Tribonacci-Lucas Numbers via the Determinants of Special Matrices, Appl. Math. Sci., 8(39), 1947–1955.
There are 10 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Barış Arslan 0000-0002-6972-3317

Kemal Uslu 0000-0001-6265-3128

Publication Date November 30, 2021
Published in Issue Year 2021 Issue: 28

Cite

APA Arslan, B., & Uslu, K. (2021). Number of Subsets of the Set [n] Including No Three Consecutive Odd Integers. Avrupa Bilim Ve Teknoloji Dergisi(28), 352-356. https://doi.org/10.31590/ejosat.999521