In this paper, we prove several identities involving linear combinations of convolutions the generalized Fibonacci and Lucas sequences. Our results apply more generally to broader classes second-order linearly recurrent sequences with constant coefficients. As a consequence, obtain as special cases many relating exactly four amongst Fibonacci, Lucas, Pell, Pell–Lucas, Jacobsthal, Jacobsthal–Luc...

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The Pell numbers, named after the English diplomat and mathematician John Pell, are studied by many authors. At this work, inspiring definition harmonic we define numbers. Moreover, construct one type of symmetric matrix family whose elements numbers its Hadamard exponential matrix. We investigate some linear algebraic properties obtain inequalities using norms. Furthermore, summation identitie...