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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 6

The Gelin-Cesaro identity in some conditional sequences

Murat ŞAHİN
Sayfa
855–861
Yayın Tarihi
2022-10-18
DOI
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Then we show that the Catalan and Gelin-Cesaro identities are satisfied by the indices of this generalized sequence.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we deal with two families of conditional sequences.
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Temel Bulgular & Veri:Also, we define a family of conditional sequences ${u_n}$by the recurrence relation ${u_n}$ = a${u_n}$−1 +${bu_n}$−2 if n is even, ${u_n}$ = ${CU_n}$−1+${du_n}$−2 if n is odd, with initial conditions ${u_o}$ = 0 and ${u_1}$ = 1, where a, b, c and d are non-zero numbers.
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Sonuç & Katkı:Then we show that the Catalan and Gelin-Cesaro identities are satisfied by the indices of this generalized sequence.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, we deal with two families of conditional sequences. The first family consists of generalizations of the Fibonacci sequence. We show that the Gelin-Ces`aro identity is satisfied. Also, we define a family of conditional sequences ${u_n}$by the recurrence relation ${u_n}$ = a${u_n}$−1 +${bu_n}$−2 if n is even, ${u_n}$ = ${CU_n}$−1+${du_n}$−2 if n is odd, with initial conditions ${u_o}$ = 0 and ${u_1}$ = 1, where a, b, c and d are non-zero numbers. Many sequences in the literature are special cases of this sequence. We find the generating function of the sequence and Binet’s formula for odd and even subscripted sequences. Then we show that the Catalan and Gelin-Cesaro identities are satisfied by the indices of this generalized sequence.

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Bu Makaleye Atıf Yap

ŞAHİN, M. (2022). The Gelin-Cesaro identity in some conditional sequences. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 6, 855–861. https://ajindex.com/articles/530574

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Kaynakça (8)

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