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: Thanks [[User:Eric Rowland]], but how would you plan to represent <math>0, 1, 0, 0, \ldots</math> as an exponential polynomial -- since <math>0^{n-1}</math> doesn't work? To exclude eventually-periodic sequences non-artificially, we just have to require that in the satisfied linear recurrence <math>s(n) = c_1 s(n-1) + c_2 s(n-2) + \dots + c_d s(n-d),</math> <math>c_d \ne 0</math>. [[User:Caleb Stanford|Caleb Stanford]] ([[User talk:Caleb Stanford|talk]]) 23:41, 7 November 2021 (UTC)
:: Good point. I checked The Concrete Tetrahedron (by Kauers and Paule), and they do require <math>c_d \ne 0</math>. This is artificial from the perspective of generating series because then the characterization as rational series needs an extra requirement on the degree of the numerator. But on the other hand it does fix the characterization as exponential polynomials. [[User:Eric Rowland|Eric Rowland]] ([[User talk:Eric Rowland|talk]]) 00:47, 8 November 2021 (UTC)
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