@article{article_999521, title={Number of Subsets of the Set [n] Including No Three Consecutive Odd Integers.}, journal={Avrupa Bilim ve Teknoloji Dergisi}, pages={352–356}, year={2021}, DOI={10.31590/ejosat.999521}, url={https://izlik.org/JA89XY54AY}, author={Arslan, Barış and Uslu, Kemal}, keywords={Tribonacci dizisi, Ardışık tek sayılar, Üreteç fonksiyon, Kombinatoryal gösterim}, 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.}, number={28}