Pascal-Like Triangles And Fibonacci-Like Sequences
MATHEMATICAL GAZETTE(2010)
Abstract
In [1] and [2] we demonstrated how Pascal-like triangles arose from the probabilities associated with the various outcomes of a particular game (see Definition 1 below). It was also shown that they could be considered as generalisations of Pascal's triangle. In this article we show how Fibonacci-like sequences arise from our Pascal-like triangles, and demonstrate the existence of simple relationships between these Fibonacci-like sequences and the Fibonacci sequence itself. In addition we will investigate a generalisation of the binomial coefficients that appears when considering an extended version of the game. We start by describing this game.
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Key words
pascal-like,fibonacci-like
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