Analysis reveals Binet-like formulas emerging from second-order linear recurrence relations, implying new insights into classical sequences.
In this paper, second-order generalized linear recurrence relations of the form Vₙ( p₁,p₂, V₁,V₂)=p₁Vₙ₋₁+p₂Vₙ₋₂ , where p₁,p₂, V₁( =a ) and V₂( =b ) are arbitrary integers, are studied to derive Binet-like formulas in simplified and comprehensive generalized forms. By imposing specific constraints on the coefficients ( p₁,p₂ ) and the initial terms ( V₁,V₂ ), various well-known existing formulas, such as those for classical Fibonacci and Lucas sequences, emerge as special cases of this generalization.
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K. L. Verma (2025) studied this question.
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