Geodesic
Jacobsthal decompositions of Pascal's triangle, ternary trees, and alternating sign matrices
Journal of integer sequences, Tome 19 (2016) no. 3
We examine Jacobsthal decompositions of Pascal's triangle and Pascal's square from a number of points of view, making use of bivariate generating functions, which we derive from a truncation of the continued fraction generating function of the Narayana number triangle. We establish links with Riordan array embedding structures. We explore determinantal links to the counting of alternating sign matrices and plane partitions and sequences related to ternary trees. Finally, we examine further relationships between bivariate generating functions, Riordan arrays, and interesting number squares and triangles.
Classification : 11C20, 11B83, 15B35, 15B36
Keywords: Jacobsthal number, Pascal's triangle, binomial matrix, Riordan array, alternating sign matrix, ternary tree, plane partition 
@article{JIS_2016__19_3_a1,
     author = {Barry,  Paul},
     title = {Jacobsthal decompositions of {Pascal's} triangle, ternary trees, and alternating sign matrices},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {3},
     zbl = {1415.11059},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_3_a1/}
}
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%T Jacobsthal decompositions of Pascal's triangle, ternary trees, and alternating sign matrices
%J Journal of integer sequences
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Barry,  Paul. Jacobsthal decompositions of Pascal's triangle, ternary trees, and alternating sign matrices. Journal of integer sequences, Tome 19 (2016) no. 3. http://geodesic.mathdoc.fr/item/JIS_2016__19_3_a1/