  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), higher-dimensional generalizations
of the Stern diatomic sequence, from the method of subdividing a triangle via
various triangle partition algorithms. We then explore several combinatorial
results about TRIP-Stern sequences, which may be used to give rise to certain
well-known sequences. We finish by generalizing TRIP-Stern sequences and
presenting analogous results for these generalizations.
