Rational Generating Functions of Numerical Sequences
Sergio Falcon *
Universidad de Las Palmas de Gran Canaria, Spain.
*Author to whom correspondence should be addressed.
Abstract
If division is performed on a rational (non-integer) function, an infinite series is obtained that is relatively easy to find. But the inverse problem can also be solved and, given an infinite numerical sequence, the rational function that that can generate it can be found. In this article, different cases are studied in which this generating function can be found in a more or less simple way.
Keywords: Generating function, recurrence relation, convolution, k-Fibonacci numbers, Extended Fibonacci numbers