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On several kinds of sums of balancing nu...
Komatsu, Takao...

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On several kinds of sums of balancing numbers by Komatsu, Takao ( Author )
Lemonjar Open Access
Australian National University
09-08-2023
The balancing numbers $B_n$ ($n=0,1,\cdots$) are solutions of the binary recurrence $B_n=6B_{n-1}-B_{n-2}$ ($n\ge 2$) with $B_0=0$ and $B_1=1$. In this paper we show several relations about the sums of product of two balancing numbers of the type $\sum_{m=0}^n B_{k m+r}B_{k(n-m)+r}$ ($k>r\ge 0$) and the alternating sum of reciprocal of balancing numbers $\left\lfloor\left(\sum_{k=n}^\infty\frac{1}{B_{l k}}\right)^{-1}\right\rfloor$. Similar results are also obtained for Lucas-balancing numbers $C_n$ ($n=0,1,\cdots$), satisfying the binary recurrence $C_n=6C_{n-1}-C_{n-2}$ ($n\ge 2$) with $C_0=1$ and $C_1=3$. Some binomial sums involving these numbers are also explored.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1608.05918
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