Ansatz in a Nutshell: A comprehensive step-by-step guide to polynomial, C-finite, holonomic, and C^2-finite sequences

Accompanied Maple program: Ansatz

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Written Jan. 16, 2022:

This is the take on the famous ansatz method (an educated guess or an additional assumption made to help solve a problem, and which may later be verified to be part of the solution by its results.)

The paper was written in a manual style that includes the commands from Maple program. We also proposed/discussed the idea of C^2-finite which generalize those existing ones.