| 摘要: |
| 设 {fn} 是双周期 Fibonacci 数列，{ln} 是双周期 Lucas 数列。本文利用 Dedekind和 S (h, k) 与双周期 Fibonacci 数列、双周期 Lucas 数列的递推公式及相关性质，得到和式 (S (f2n, f2n+1) + S (f2n+1, f2n+2)) 与 (S (l2n, l2n+1) + S (l2n+1, l2n+2)) 的估计式. 将涉及 Dedekind 和的线性递推数列的研究推广到了非线性. |
| 关键词: 双周期 Fibonacci 数列 双周期 Lucas 数列 Dedekind 和 |
| DOI： |
| 分类号:O156.4 |
| 基金项目:国家自然科学基金项目资助 (12126357). |
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| The Dedekind sums involving bi-periodic Fibonacci and Lucas sequences |
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Du Tingting, Liu Xiaoge
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.Research Center for Number Theory and Its Applications, Northwest University, Xi’an, 710127, China
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| Abstract: |
| Let {fn} be the bi-periodic Fibonacci sequence and {ln} be the bi-periodic Lucas sequence. In this paper, by using the recurrence formula and related properties of Dedekind sums S (h, k) and bi-periodic Fibonacci sequence and bi-periodic Lucas sequence, We get the estimated
results of (S (f2n, f2n+1) + S (f2n+1, f2n+2)) and (S (l2n, l2n+1) + S (l2n+1, l2n+2)). The research of linear recurrence sequences involving Dedekind sums has been extended to the nonlinear case. |
| Key words: Bi-periodic Fibonacci sequence Bi-periodic Lucas sequence Dedekind sums. |
