\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
\BOOKMARK [1][-]{section.2}{Continued fractions and Stern's diatomic sequence}{}% 2
\BOOKMARK [2][-]{subsection.2.1}{Continued fractions and subdivisions of the unit interval}{section.2}% 3
\BOOKMARK [2][-]{subsection.2.2}{Stern's diatomic sequence}{section.2}% 4
\BOOKMARK [1][-]{section.3}{Review of triangle partition maps}{}% 5
\BOOKMARK [2][-]{subsection.3.1}{The triangle division}{section.3}% 6
\BOOKMARK [2][-]{subsection.3.2}{Incorporating permutations}{section.3}% 7
\BOOKMARK [2][-]{subsection.3.3}{TRIP sequences}{section.3}% 8
\BOOKMARK [1][-]{section.4}{TRIP-Stern sequences}{}% 9
\BOOKMARK [2][-]{subsection.4.1}{Construction of TRIP-Stern sequences}{section.4}% 10
\BOOKMARK [2][-]{subsection.4.2}{Examples}{section.4}% 11
\BOOKMARK [2][-]{subsection.4.3}{Alternative definitions}{section.4}% 12
\BOOKMARK [1][-]{section.5}{A more pictorial approach}{}% 13
\BOOKMARK [1][-]{section.6}{Maximum terms and positions thereof}{}% 14
\BOOKMARK [2][-]{subsection.6.1}{Explicit formulas and recurrence relations for sequences of maximal terms}{section.6}% 15
\BOOKMARK [1][-]{section.7}{Minimal terms and positions thereof}{}% 16
\BOOKMARK [1][-]{section.8}{Level sums}{}% 17
\BOOKMARK [2][-]{subsection.8.1}{Level sums for \(e,e,e\)}{section.8}% 18
\BOOKMARK [2][-]{subsection.8.2}{Level sums for arbitrary \(,0,1\)}{section.8}% 19
\BOOKMARK [3][-]{subsubsection.8.2.1}{Six row sum recurrence relations already well-known}{subsection.8.2}% 20
\BOOKMARK [1][-]{section.9}{Forbidden triples for \(e,e,e\)}{}% 21
\BOOKMARK [1][-]{section.10}{Generalized TRIP-Stern sequences}{}% 22
\BOOKMARK [2][-]{subsection.10.1}{Construction of generalized TRIP-Stern sequences}{section.10}% 23
\BOOKMARK [2][-]{subsection.10.2}{Maximum terms and positions thereof for generalized TRIP-Stern sequences}{section.10}% 24
\BOOKMARK [2][-]{subsection.10.3}{Minimal terms and positions thereof}{section.10}% 25
\BOOKMARK [2][-]{subsection.10.4}{Level sums for generalized TRIP-Stern sequences}{section.10}% 26
\BOOKMARK [1][-]{section.11}{Conclusion}{}% 27
\BOOKMARK [1][-]{section.12}{Acknowledgments}{}% 28