IDENTITIES INVOLVING THE TRIBONACCI NUMBERS SQUARED VIA TILING WITH COMBS
The number of ways to tile an n-board (an n×1 rectangular board) with (2112 ; 1)-, (2112 ; 2)-, and (2112 ; 3)-combs is Tn2+2, where Tn is the nth tribonacci number. A (2112 ; m)comb is a tile composed of m sub-tiles of dimensions 12 × 1 (with the shorter sides always horizontal) separated by gaps o...
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th-mahidol.880432023-07-24T01:01:36Z IDENTITIES INVOLVING THE TRIBONACCI NUMBERS SQUARED VIA TILING WITH COMBS Allen M.A. Mahidol University Mathematics The number of ways to tile an n-board (an n×1 rectangular board) with (2112 ; 1)-, (2112 ; 2)-, and (2112 ; 3)-combs is Tn2+2, where Tn is the nth tribonacci number. A (2112 ; m)comb is a tile composed of m sub-tiles of dimensions 12 × 1 (with the shorter sides always horizontal) separated by gaps of dimensions 21 × 1. We use such tilings to obtain quick combinatorial proofs of identities relating the tribonacci numbers squared to one another, to other combinations of tribonacci numbers, and to the Fibonacci, Narayana’s cows, and Padovan numbers. Most of these identities appear to be new. 2023-07-23T18:01:36Z 2023-07-23T18:01:36Z 2023-02-01 Article Fibonacci Quarterly Vol.61 No.1 (2023) , 21-27 00150517 2-s2.0-85164811579 https://repository.li.mahidol.ac.th/handle/123456789/88043 SCOPUS |
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Mahidol University |
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Mahidol University Library |
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Asia |
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Thailand Thailand |
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Mathematics |
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Mathematics Allen M.A. IDENTITIES INVOLVING THE TRIBONACCI NUMBERS SQUARED VIA TILING WITH COMBS |
| description |
The number of ways to tile an n-board (an n×1 rectangular board) with (2112 ; 1)-, (2112 ; 2)-, and (2112 ; 3)-combs is Tn2+2, where Tn is the nth tribonacci number. A (2112 ; m)comb is a tile composed of m sub-tiles of dimensions 12 × 1 (with the shorter sides always horizontal) separated by gaps of dimensions 21 × 1. We use such tilings to obtain quick combinatorial proofs of identities relating the tribonacci numbers squared to one another, to other combinations of tribonacci numbers, and to the Fibonacci, Narayana’s cows, and Padovan numbers. Most of these identities appear to be new. |
| author2 |
Mahidol University |
| author_facet |
Mahidol University Allen M.A. |
| format |
Article |
| author |
Allen M.A. |
| author_sort |
Allen M.A. |
| title |
IDENTITIES INVOLVING THE TRIBONACCI NUMBERS SQUARED VIA TILING WITH COMBS |
| title_short |
IDENTITIES INVOLVING THE TRIBONACCI NUMBERS SQUARED VIA TILING WITH COMBS |
| title_full |
IDENTITIES INVOLVING THE TRIBONACCI NUMBERS SQUARED VIA TILING WITH COMBS |
| title_fullStr |
IDENTITIES INVOLVING THE TRIBONACCI NUMBERS SQUARED VIA TILING WITH COMBS |
| title_full_unstemmed |
IDENTITIES INVOLVING THE TRIBONACCI NUMBERS SQUARED VIA TILING WITH COMBS |
| title_sort |
identities involving the tribonacci numbers squared via tiling with combs |
| publishDate |
2023 |
| url |
https://repository.li.mahidol.ac.th/handle/123456789/88043 |
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1781414987996069888 |