  Linear recurrence equations with constant coefficients define the power
series coefficients of rational functions. However, one usually prefers to have
an explicit formula for the sequence of coefficients, provided that such a
formula is "simple" enough. Simplicity is related to the compactness of the
formula due to the presence of algebraic numbers: "the smaller, the simpler".
This poster showcases the capacity of recent updates on the Formal Power Series
(FPS) algorithm, implemented in Maxima and Maple (convert/FormalPowerSeries),
to find simple formulas for sequences like those from https://oeis.org/A307717,
https://oeis.org/A226782, or https://oeis.org/A226784 by computing power series
representations of their correctly guessed generating functions. We designed
the algorithm for the more general context of univariate $P$-recursive
sequences. Our implementations are available at
http://www.mathematik.uni-kassel.de/~bteguia/FPS_webpage/FPS.htm

Symbolic Computation;Combinatorics