Geodesic
Stern sequences for a family of multidimensional continued fractions: TRIP-Stern sequences
Journal of integer sequences, Tome 20 (2017) no. 1
The Stern diatomic sequence is closely linked to continued fractions via the Gauss map on the unit interval, which in turn can be understood via systematic subdivisions of the unit interval. Higher-dimensional analogues of continued fractions, called multidimensional continued fractions, can be produced through various subdivisions of a triangle. We define triangle partition-Stern sequences (TRIP-Stern sequences for short) from certain triangle divisions developed earlier by the authors. These sequences are higher-dimensional generalizations of the Stern diatomic sequence. We then prove several combinatorial results about TRIP-Stern sequences, many of which give rise to well-known sequences. We finish by generalizing TRIP-Stern sequences and presenting analogous results for these generalizations.
Classification : 11B83, 11A55, 11J70, 40A99
Keywords: stern's diatomic sequence, multidimensional continued fraction 
@article{JIS_2017__20_1_a5,
     author = {Amburg,  Ilya and Dasaratha,  Krishna and Flapan,  Laure and Garrity,  Thomas and Lee,  Chansoo and Mihaila,  Cornelia and Neumann-Chun,  Nicholas and Peluse,  Sarah and Stoffregen,  Matthew},
     title = {Stern sequences for a family of multidimensional continued fractions: {TRIP-Stern} sequences},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {1},
     zbl = {1420.11054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_1_a5/}
}
TY  - JOUR
AU  - Amburg,  Ilya
AU  - Dasaratha,  Krishna
AU  - Flapan,  Laure
AU  - Garrity,  Thomas
AU  - Lee,  Chansoo
AU  - Mihaila,  Cornelia
AU  - Neumann-Chun,  Nicholas
AU  - Peluse,  Sarah
AU  - Stoffregen,  Matthew
TI  - Stern sequences for a family of multidimensional continued fractions: TRIP-Stern sequences
JO  - Journal of integer sequences
PY  - 2017
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JIS_2017__20_1_a5/
LA  - en
ID  - JIS_2017__20_1_a5
ER  - 
%0 Journal Article
%A Amburg,  Ilya
%A Dasaratha,  Krishna
%A Flapan,  Laure
%A Garrity,  Thomas
%A Lee,  Chansoo
%A Mihaila,  Cornelia
%A Neumann-Chun,  Nicholas
%A Peluse,  Sarah
%A Stoffregen,  Matthew
%T Stern sequences for a family of multidimensional continued fractions: TRIP-Stern sequences
%J Journal of integer sequences
%D 2017
%V 20
%N 1
%U http://geodesic.mathdoc.fr/item/JIS_2017__20_1_a5/
%G en
%F JIS_2017__20_1_a5
Amburg,  Ilya; Dasaratha,  Krishna; Flapan,  Laure; Garrity,  Thomas; Lee,  Chansoo; Mihaila,  Cornelia; Neumann-Chun,  Nicholas; Peluse,  Sarah; Stoffregen,  Matthew. Stern sequences for a family of multidimensional continued fractions: TRIP-Stern sequences. Journal of integer sequences, Tome 20 (2017) no. 1. http://geodesic.mathdoc.fr/item/JIS_2017__20_1_a5/