On Three Consecutive Pairs of Lucas and Fibonacci Numbers Connected to Pell-lucas and Pell Polynomials
Year: 2025
Type: article
Abstract: In the present paper we connect three consecutive pairs of Lucas and Fibonacci numbers, namely, { ( L 3 n , F 3 n ) , ( L 3 n +1 , F 3 n +1 ) , ( L 3 n +2 , F 3 n +2 ) : n = 0 , 1 , 2 , 3 , ···} to Pell-Lucas and Pell polyno- mials, namely, P n ( x ) = 1 2 h x + p x 2 + 1 n + x − p x 2 + 1 n i and Q n ( x ) = 1 2 √ x 2 + 1 h x + p x 2 + 1 n − x − p x 2 + 1 n i . We workout some interesting combinatorial identities of X n = P n (2) , Y n = Q n (2) and the three consec- utive pairs of Lucas and Fibonacci numbers
Authors: GOUTHAM C, R. RANGARAJAN
Institution: University of Mysore
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W6930850439
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