Fibonacci, Lucas, and the ubiquitous Catalan numbers are delightful sources for experimentation, exploration, and conjecture (Askey 2005; Koshy 2001, 2006, 2008). Pell numbers are another similarly rich source. In this article, I will demonstrate some patterns associated with Pell numbers and then will show how they can be extracted from Pascal and Pascal–like triangles. I will provide a geometric interpretation of Pell numbers and conclude by citing a few opportunities for further exploration.
Thomas Koshy, firstname.lastname@example.org, is professor of mathematics at Framingham State University in Massachusetts. An author of several books, including Fibonacci Numbers with Applications (Wiley 2001) and Catalan Numbers with Applications (Oxford 2009), he teaches number theory to prospective and in-service middle school and high school teachers.