Demetrios L. Antzoulakos, "Extended Fibonacci numbers and polynomials with probability applications", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 134012, 13 pages, 2004. https://doi.org/10.1155/S016117120440458X
Extended Fibonacci numbers and polynomials with probability applications
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.
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