Sums of products of binomial coefficients mod 2 and run length transforms of sequences
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arXiv
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| Format: | Preprint |
| Published: |
2016
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| _version_ | 1866912702444601344 |
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| author | Wu, Chai Wah |
| author_facet | Wu, Chai Wah |
| contents | We study properties of functions of binomial coefficients mod 2 and derive a set of recurrence relations for sums of products of binomial coefficients mod 2. We show that they result in sequences that are the run length transforms of well known basic sequences. In particular, we obtain formulas for the run length transform of the positive integers, Fibonacci numbers, extended Lucas numbers and Narayana's cows sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1610_06166 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Sums of products of binomial coefficients mod 2 and run length transforms of sequences Wu, Chai Wah Combinatorics 11B30 We study properties of functions of binomial coefficients mod 2 and derive a set of recurrence relations for sums of products of binomial coefficients mod 2. We show that they result in sequences that are the run length transforms of well known basic sequences. In particular, we obtain formulas for the run length transform of the positive integers, Fibonacci numbers, extended Lucas numbers and Narayana's cows sequence. |
| title | Sums of products of binomial coefficients mod 2 and run length transforms of sequences |
| topic | Combinatorics 11B30 |
| url | https://arxiv.org/abs/1610.06166 |