Definition:Fibonomial Triangle
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Definition
The Fibonomial triangle is an array formed by the Fibonomial coefficients:
- $\begin{array}{r|rrrrrrrrrr} n & \binom n 0_\FF & \binom n 1_\FF & \binom n 2_\FF & \binom n 3_\FF & \binom n 4_\FF & \binom n 5_\FF & \binom n 6_\FF \\ \hline 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & \\ 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & \\ 2 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & \\ 3 & 1 & 2 & 2 & 1 & 0 & 0 & 0 & \\ 4 & 1 & 3 & 6 & 3 & 1 & 0 & 0 & \\ 5 & 1 & 5 & 15 & 15 & 5 & 1 & 0 & \\ 6 & 1 & 8 & 40 & 60 & 40 & 8 & 1 & \\ \end{array}$
This sequence is A010048 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.8$: Fibonacci Numbers: Exercise $29 \ \text{(a)}$