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{{ping|D.Lazard}} --- Your input would also be valuable here. As Eric points out, the whole article is about sequences, not solving recurrences, so the new name does not fit. I am thinking that having 2 articles would therefore be best as above. [[User:Caleb Stanford|Caleb Stanford]] ([[User talk:Caleb Stanford|talk]]) 13:03, 22 November 2021 (UTC)
I agree that 3 articles is a lot, but these objects are so common that they occur in lots of different areas, so different people have quite different ways of thinking about them and different aspects they are interested in. A similar situation exists with [[P-recursive equation]], [[Polynomial solutions of P-recursive equations]], [[Holonomic function]], and [[Linear differential equation]] (though in this case hopefully we can reduce the number of articles). [[Linear difference equation]] seems to be focused on models and stability, which is different than what combinatorists and computer scientists might be interested in. I propose leaving it as its own article and trying to avoid too much duplication where it makes sense. Most of the material under [[Recurrence relation#Solving homogeneous linear recurrence relations with constant coefficients]] could be merged into one of the other two articles since [[Recurrence relation]] is quite long.
As for terminology, the reasoning "'''linear-recursive''' is used extensively throughout the article" applies equally well to '''constant-recursive''' because all instances of "constant-recursive" were replaced with "linear-recursive" when the title was changed. So I still don't see good motivation for the recent renaming. The unfortunate fact is that there is no one established name for these sequences. "linear-recursive" is not great because it doesn't distinguish between recurrences with constant coefficients and recurrences with polynomials coefficients where <math>s(n + i)</math> also appear linearly. "constant-recursive"/"C-recursive"/"C-finite" are used less widely but have the advantages that they make this distinction and they parallel "polynomial-recursive"/"P-recursive". [[User:Eric Rowland|Eric Rowland]] ([[User talk:Eric Rowland|talk]]) 16:37, 22 November 2021 (UTC)
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