  The close relationship among the polynomial functions and Fibonacci numerical
sequences is shown in this paper. These numerical sequences are defined by the
recurrence equation $x_{k + n} = \displaystyle\sum_{j = 0}^{n-1}\alpha_j x_{k +
j}$, where $n$ is the polynomial degree and $\alpha$'s, the polynomial
coefficients. The arithmetic trapezoid resulting from the recurrence equations
is also shown. This trapezoid is nothing but a generalization of Pascal's
Triangle. Trapezoid is a convenient name because the form it appears does not
have the `upper end` of a usual triangle. This study shows that each polynomial
generates infinite sequences, and that each sequence generates only a single
arithmetic trapezoid.
