Sukanya Somprom, Waitaya Nimnual, Wathcharapong Hongthong, "Some Identities for an Alternating Sum of Fibonacci and Lucus Numbers of Order k," WSEAS Transactions on Mathematics, vol. 21, pp. 580-584, 2022, DOI:10.37394/23206.2022.21.65
Sukanya Somprom, Waitaya Nimnual, Wathcharapong Hongthong. Some Identities for an Alternating Sum of Fibonacci and Lucus Numbers of Order k.
WSEAS Transactions on Mathematics. 2022;21:580-584. 10.37394/23206.2022.21.65
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 21, 2022
Some Identities for an Alternating Sum of Fibonacci and Lucus Numbers of Order k
Authors: , ,
Abstract: In this paper, we defined $$F^{(k)}_{n}$$ be the Fibonacci of order $$k$$ and $$L^{(k)}_{n}$$ be the Lucas number of order
$$k$$. We presented some of their new identities as well as some results of relation for an alternating sum between
Fibonacci and Lucas number of order $$k$$ as follow; <br>
$$\displaystyle\sum\limits_{i=0}^n (-1)^{i}m^{n-1}(mL^{(k)}_{i+1}+((m-2)^2-4)F^{(k)}_{i}-2m^2F^{(k)}_{i-1}-m\displaystyle\sum\limits_{j=3}^k jF^{(k)}_{i-j+2}=(-1)^nm(F^{(k)}_{n+1}-2F^{(k)}_{n})$$.
Keywords:
Alternating sums, Fibonacci number of order $$k$$, Lucas number of order $$k$$, Tribonacci number
Pages: 580-584 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 21, 2022, Art. #65 DOI: 10.37394/23206.2022.21.65
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