Residue Counts Modulo Three for the Fibonacci Triangle

Diana L. Wells

A chapter in Applications of Fibonacci Numbers, 1996, pp 521-536 from Springer

Abstract: Abstract The Fibonacci Triangle is formed in a manner similar to that of Pascal’s Triangle. The entries in Pascal’s Triangle are the binomial coefficients, whereas the entries in the Fibonacci Triangle are the Fibonacci coefficients defined by, $$ {\left[ {\begin{array}{*{20}{c}} n \\ k \end{array}} \right]_F} = \frac{{{F_n}{F_{n - 1}} \cdots {F_1}}}{{\left( {{F_k}{F_{k - 1}} \cdots {F_1}} \right)\left( {{F_{n - k}}{F_{n - k - 1}} \cdots {F_1}} \right),}} $$ where $$ \mathcal{F} = \left\{ {{F_j}} \right\}$$ is the Fibinacci Sequence.

Date: 1996
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DOI: 10.1007/978-94-009-0223-7_42

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