A generalization of André-Jeannin’s symmetric identity - Munarini, Emanuele (Pure mathematics and applications, 2018)
In 1997, Richard André-Jeannin obtained a symmetric identity involving the reciprocal of the Horadam numbers , defined by a three-term recurrence = with constant coefficients. In this paper, we extend this identity to sequences satisfying a three-term recurrence = + with arbitrary coefficients. Then, we specialize such an identity to several -polynomials of combinatorial interest, such as the -Fibonacci, -Lucas, -Pell, -Jacobsthal, -Chebyshev and -Morgan-Voyce polynomials.