Sequences of numbers meet the generalized Gegenbauer-Humbert polynomials (Q410665)

Summary: Here we present a connection between a sequence of numbers generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer-Humbert polynomials. Many new and known formulas of Fibonacci, Lucas, Pell, and Jacobsthal numbers in terms of generalized Gegenbauer-Humbert polynomial values are given. The applications of the relationship to the construction of identities of number and polynomial value sequences defined by linear recurrence relations are also discussed.