On integer-sequence-based constructions of generalized pascal triangles

Paul Barry

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1-34
Number of pages34
JournalJournal of Integer Sequences
Volume9
Issue number2
Publication statusPublished - 19 May 2006

Keywords

  • Catalan numbers
  • Delannoy numbers
  • Fibonacci numbers
  • Jacobsthal numbers
  • Narayana numbers
  • Pascal's triangle
  • Schröder numbers

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