Geodesic
Analytic representations of the \(n\)-anacci constants and generalizations thereof
Journal of integer sequences, Tome 18 (2015) no. 4
We study generalizations of the sequence of the $n$-anacci constants that are constructed from the ratio limits generated by linear recurrences of an arbitrary order $n$ with equal integer weights $m$. We derive the analytic representation of the class $C^{\infty }$ of these ratio limits and prove that, for a fixed $m$, the ratio limits form a strictly increasing sequence converging to $m+1$. We also show that the generalized $n$-anacci constants form a totally ordered set.
Classification : 11B37, 11B39
Keywords: linear recurrence, n-step Fibonacci number, weighted n-generalized Fibonacci sequence, generalized n-anacci constant 
@article{JIS_2015__18_4_a1,
     author = {Szczyrba,  Igor and Szczyrba,  Rafa{\l} and Burtscher,  Martin},
     title = {Analytic representations of the \(n\)-anacci constants and generalizations thereof},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {4},
     zbl = {1378.11023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_4_a1/}
}
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Szczyrba,  Igor; Szczyrba,  Rafał; Burtscher,  Martin. Analytic representations of the \(n\)-anacci constants and generalizations thereof. Journal of integer sequences, Tome 18 (2015) no. 4. http://geodesic.mathdoc.fr/item/JIS_2015__18_4_a1/