The Polynomial Sequence Generalizing the Integer Sequence which Enumerates the Number of Subsets of the Set [n] Including No Two Consecutive Even Integers

Year 2022, Issue: 34, 164 - 169, 31.03.2022

Barış Arslan Kemal Uslu

https://doi.org/10.31590/ejosat.1078691

Abstract

Fibonacci polynomial sequence is an extension of Fibonacci sequence. Here we define a polynomial sequence generalizing the integer sequence which enumerates the number of subsets of the set [n] including no two consecutive even integers. The polynomial sequence is associated with the Fibonacci polynomials. Some basic properties of the polynomial sequence are obtained.

Keywords

Fibonacci numbers, Fibonacci polynomials, Polynomial sequence, Consecutive even integers, Generating function, Combinatorial representation

[n] Kümesinin Ardışık İki Çift Tamsayı İçermeyen Alt Kümelerinin Sayısını Veren Tamsayı Dizisini Genelleyen Polinom Dizisi

Abstract

Fibonacci polinom dizisi Fibonacci dizisinin bir genişlemesidir. Burada [n] kümesinin ardışık iki tamsayı içermeyen alt kümelerinin sayısını veren tamsayı dizisini genelleyen bir polinom dizisi tanımladık. Bu polinom dizisi Fibonacci polinomları ile ilişkilendirildi. Polinom dizisinin bazı temel özellikleri elde edildi.

Keywords

Fibonacci sayıları, Fibonacci Polinomları, Polinom dizisi, Ardışık çift sayılar, Üreteç fonksiyon, Kombinatoryal gösterim

References

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