On Some Identities of Balancing-Like and Lucas-Balancing-Like Sequences by the Matrix Method

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Sanit Ritthidej
Theerapon Buatong
Sirachat Tipsri


Balancing-like and Lucas-balancing-like sequences are defined by gif.latex?\left&space;\{&space;\frac{\sigma&space;_k}{2}&space;\right&space;\}  and gif.latex?\left&space;\{&space;N_k&space;\right&space;\}  for positive integer gif.latex?k , respectively,  for gif.latex?N_k and gif.latex?\sigma&space;_k  are solutions of Pell’s equation gif.latex?N^2-12\sigma^2=1. These sequences are determined as the linear recurrence relations gif.latex?L_{n+1}=4L_{n}-L_{n-1}  and gif.latex?M_{n+1}=4M_{n}-M_{n-1}  with initial conditions gif.latex?L_{0}=0,L_{1}=1 and gif.latex?M_{0}=1,M_{1}=2  for positive integer gif.latex?n  , respectively. In this paper, some identities of Balancing-like and Lucas-balancing-like sequences are obtained by using Binet’s formulas which are formulated by matrices gif.latex?Q_{L} and gif.latex?Q_{M}.

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Ritthidej, S., Buatong, T., & Tipsri, S. (2023). On Some Identities of Balancing-Like and Lucas-Balancing-Like Sequences by the Matrix Method. PKRU SciTech Journal, 7(2), 37–48. Retrieved from https://ph01.tci-thaijo.org/index.php/pkruscitech/article/view/252191
Research Articles


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