# Fibonacci and Lucas Numbers

@inproceedings{Hilton1997FibonacciAL, title={Fibonacci and Lucas Numbers}, author={Peter J. Hilton and Derek A. Holton and Jean J. Pedersen}, year={1997} }

Consider the following number trick–try it out on your friends. You ask them to write down the numbers from 0 to 9. Against 0 and 1 they write any two numbers (we suggest two fairly small positive integers just to avoid tedious arithmetic, but all participants should write the same pair of numbers). Then against 2 they write the sum of the entries against 0 and 1; against 3 they write the sum of the entries against 1 and 2; and so on. Once they have completed the process, producing entries…

## 169 Citations

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We explore the sums of k consecutive terms in the generalized Fibonacci sequence ( G n ) n ≥ 0 given by the recurrence G n = G n − 1 + G n − 2 for all n ≥ 2 with integral initial conditions G 0 and G…

### Sums of certain products of Fibonacci and Lucas numbers

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### INITIAL DIGITS IN NUMBER THEORY

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1. J. C. Butcher. "On a Conjecture Concerning a Set of Sequences Satisfying The Fibonacci Difference Equation/ The Fibonacci Quarterly 16 (1978):8183. 2. M. D. Hendy, "Stolarskys Distribution of…

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