Year: 2025
Type: article
Abstract: For an integer $$k\ge 2$$ k ≥ 2 , let $$(P^{(k)}_{n})_n$$ ( P n ( k ) ) n be the k -generalized Pell sequence whose first k terms are $$0,\ldots , 0, 1$$ 0 , … , 0 , 1 and each term afterwards is given by the k th order linear recurrence $$P^{(k)}_{n}=2P^{(k)}_{n-1}+P^{(k)}_{n-2} +\cdots +P^{(k)}_{n-k}$$ P n ( k ) = 2 P n - 1 ( k ) + P n - 2 ( k ) + ⋯ + P n - k ( k ) . For the usual Pell sequence $$(P_n)_n=(P^{(2)}_{n})_n$$ ( P n ) n = ( P n ( 2 ) ) n the formula $$P_{n}^2+P_{n+1}^2=P_{2n+1}$$ P n 2 + P n + 1 2 = P 2 n + 1 holds for all $$n\ge 0$$ n ≥ 0
Authors: Jhon J. Bravo, Florian Luca, Fabian Pomeo
Institutions: University of Cauca, Stellenbosch University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Funder: Universidad del Cauca
OpenAlex ID: W4415443876