Thomas A. Dowling

Department of Mathematics

Ohio State University

Columbus, OH 43210-1174

Douglas R. Shier

Department of Mathematical Sciences

Clemson University

Clemson, SC 29634-0975

Abstract: This section discusses different representations for sequences, such as using a closed form, a generating function, or a recurrence relation. Properties, key features, and applications are discussed for a variety of important integer sequences: Fibonacci, Lucas, Catalan, Bernoulli, Eulerian, and Ramsey numbers, among others. In addition, a miniguide to integer sequences is presented, classified according to the type of combinatorial structure that produces the terms.

Key Words: Bernoulli numbers, Bernoulli polynomials, Catalan numbers, De Bruijn numbers, Eulerian numbers, Fibonacci numbers, Gray codes, Lah coefficients, Lucas numbers, Ramsey numbers