Abstract
There is a vast array of integer sequences, many of which display interesting patterns and a number of fascinating properties. Quite a few of them are within reach of high school students and certainly number-theoretic enthusiasts. The Fibonacci and Lucas sequences, for example, are two of the most popular and delightful number sequences. Their beauty and ubiquity continue to amaze the mathematics community.
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Notes
- 1.
RHS and LHS are abbreviations of right-hand side and left-hand side, respectively.
- 2.
\(t_{n} = \frac{n(n+1)} {2}\) is the nth triangular number.
- 3.
The parenthesized bi-level notation was introduced by the German mathematician and physicist Andreas von Ettinghausen (1796–1878) in his book Die Combinatorische Analysis, published in 1826. It is also denoted by C(n, r) and nCr.
- 4.
The number α is the well-known golden ratio, \(\alpha +\beta = 1\), and \(\alpha \beta = -1\).
- 5.
McCarthy coined the term artificial intelligence while at Dartmouth College, New Hampshire.
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Koshy, T. (2014). Fundamentals. In: Pell and Pell–Lucas Numbers with Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8489-9_1
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