© Hindawi Publishing Corp. EXTENDED FIBONACCI NUMBERS AND POLYNOMIALS WITH PROBABILITY APPLICATIONS

Abstract

The extended Fibonacci sequence of numbers and polynomials is introduced and studied. The generating function, recurrence relations, an expansion in terms of multinomial coefficients, and several properties of the extended Fibonacci numbers and polynomials are obtained. Interesting relations between them and probability problems which take into account lengths of success and failure runs are also established. 2000 Mathematics Subject Classification: 62E15, 11B39, 60C05