Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4

On Integer-Sequence-Based Constructions of Generalized Pascal Triangles

Paul Barry
School of Science
Waterford Institute of Technology
Ireland

Abstract: 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.

(Concerned with sequences A000045 A000108 A000129 A000891 A000984 A001003 A001045 A001263 A001700 A001850 A002002 A003150 A005568 A006318 A007318 A007564 A008288 A009545 A010048 A015056 A015109 A016116 A047891 A056939 A056940 A059231 A060693 A078009 A078018 A081178 A081577 A081578 A081579 A081580 A082147 A082148 A082181 A082201 A082301 A082302 A082305 A082366 A082367 A087647 A088218 A088617 A088855 A114197 A114198 A114202 and A117401 .)

Received December 7 2005; revised version received April 21 2006. Published in Journal of Integer Sequences May 19 2006.