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- W2336889088 abstract "The Fibonacci sequence $mathbb{F}$ is the fixed point beginning with $a$ of morphism $sigma(a,b)=(ab,a)$. Since $mathbb{F}$ is uniformly recurrent, each factor $omega$ appears infinite many times in the sequence which is arranged as $omega_p$ $(pge 1)$. Here we distinguish $omega_pneqomega_q$ if $pneq q$. In this paper, we give algorithm for counting the number of repeated palindromes in $mathbb{F}[1,n]$ (the prefix of $mathbb{F}$ of length $n$). That is the number of the pairs $(omega, p)$, where $omega$ is a palindrome and $omega_pprecmathbb{F}[1,n]$. We also get explicit expressions for some special $n$ such as $n=f_m$ (the $m$-th Fibonacci number). The similar results are also given to the Tribonacci sequence, the fixed point beginning with $a$ of morphism $tau(a,b,c)=(ab,ac,a)$." @default.
- W2336889088 created "2016-06-24" @default.
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- W2336889088 date "2016-04-18" @default.
- W2336889088 modified "2023-09-23" @default.
- W2336889088 title "The numbers of repeated palindromes in the Fibonacci and Tribonacci sequences" @default.
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