Geodesic
On integer-sequence-based constructions of generalized Pascal triangles
Journal of integer sequences, Tome 9 (2006) no. 2
We introduce an integer sequence based construction of invertible centrally symmetric number triangles, which generalize Pascal's triangle. We characterize the row sums and central coefficients of these triangles, and examine other properties. Links to the Narayana numbers are explored. Use is made of the Riordan group to elucidate properties of a special one-parameter subfamily. An alternative exponential approach to constructing generalized Pascal triangles is briefly explored.
Classification : 11B83, 05A19, 11B37, 11B65
Keywords: Pascal's triangle, narayana numbers, Catalan numbers, schr$\ddot $oder numbers, de- lannoy numbers, Fibonacci numbers, jacobsthal numbers 
@article{JIS_2006__9_2_a5,
     author = {Barry,  Paul},
     title = {On integer-sequence-based constructions of generalized {Pascal} triangles},
     journal = {Journal of integer sequences},
     year = {2006},
     volume = {9},
     number = {2},
     zbl = {1178.11023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2006__9_2_a5/}
}
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Barry,  Paul. On integer-sequence-based constructions of generalized Pascal triangles. Journal of integer sequences, Tome 9 (2006) no. 2. http://geodesic.mathdoc.fr/item/JIS_2006__9_2_a5/