A pascal-like triangle related to the tribonacci numbers
A tile composed of two pieces, which we refer to as a fence tile, is introduced to give the Tribonacci numbers a new combinatorial interpretation. The interpretation is used to construct a Pascal-like triangle and various identities concerning the triangle are proven. An intuitive proof of a general...
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| Format: | Article |
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2018
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| Online Access: | https://repository.li.mahidol.ac.th/handle/123456789/19419 |
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| Institution: | Mahidol University |
| Summary: | A tile composed of two pieces, which we refer to as a fence tile, is introduced to give the Tribonacci numbers a new combinatorial interpretation. The interpretation is used to construct a Pascal-like triangle and various identities concerning the triangle are proven. An intuitive proof of a general identity for the Tribonacci numbers in terms of sums of products of the binomial coefficients is given. A connection with sequence A120415 from Sloane's Encyclopedia of Integer Sequences is also made. |
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