Geodesic
Largest values of the Stern sequence, alternating binary expansions and continuants
Journal of integer sequences, Tome 20 (2017) no. 2
We study the largest values of the $r$th row of Stern's diatomic array. In particular, we prove some conjectures of Lansing. Our main tool is the connection between the Stern sequence, alternating binary expansions, and continuants. This allows us to reduce the problem of ordering the elements of the Stern sequence to the problem of ordering continuants. We describe an operation that increases the value of a continuant, allowing us to reduce the problem of largest continuants to ordering continuants of very special shape. Finally, we order these special continuants using some identities and inequalities involving Fibonacci numbers.
Keywords: stern sequence, alternating binary expansion, continuant 
@article{JIS_2017__20_2_a7,
     author = {Paulin,  Roland},
     title = {Largest values of the {Stern} sequence, alternating binary expansions and continuants},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {2},
     zbl = {1420.11016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_2_a7/}
}
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Paulin,  Roland. Largest values of the Stern sequence, alternating binary expansions and continuants. Journal of integer sequences, Tome 20 (2017) no. 2. http://geodesic.mathdoc.fr/item/JIS_2017__20_2_a7/