Geodesic
Positivity of three-term recurrence sequences
The electronic journal of combinatorics, Tome 17 (2010)
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In this paper, we give the sufficient conditions for the positivity of recurrence sequences defined by $$a_nu_{n}=b_nu_{n-1}-c_nu_{n-2}$$ for $n\geqslant 2$, where $a_n,b_n,c_n$ are all nonnegative and linear in $n$. As applications, we show the positivity of many famous combinatorial sequences.
DOI : 10.37236/329
Classification : 11B37, 05A20
Mots-clés : recursions, positive sequences, log convex sequences, log concave sequences, special functions, lattice walks 
@article{10_37236_329,
     author = {Lily L. Liu},
     title = {Positivity of three-term recurrence sequences},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/329},
     zbl = {1219.11022},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/329/}
}
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%A Lily L. Liu
%T Positivity of three-term recurrence sequences
%J The electronic journal of combinatorics
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Lily L. Liu. Positivity of three-term recurrence sequences. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/329

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