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

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.

Keywords

• Tribonacci sequence
• Consecutive odd integers
• Generating function
• Combinatorial representation

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

Öz

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.

Anahtar Kelimeler

• Tribonacci dizisi
• Ardışık tek sayılar
• Üreteç fonksiyon
• Kombinatoryal gösterim

Kaynakça

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