A Combinatorial Proof of a Result on Generalized Lucas Polynomials
We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2016-09-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/dema.2016.49.issue-3/dema-2016-0022/dema-2016-0022.xml?format=INT |
| Summary: | We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively. |
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| ISSN: | 0420-1213 2391-4661 |