On the Recursive Sequence xn+1=xn−k+11+xnxn−1…xn−k$$ {x}_{n+1}=\frac{x_{n-\left(k+1\right)}}{1+{x}_n{x}_{n-1}\dots {x}_{n-k}} $$
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DOI: 10.1007/s10958-018-3982-y
Abstract: A solution of the following difference equation is investigated:xn+1=xn−k+11+xnxn−1…xn−k,n=0,1,2,…$$ {x}_{n+1}=\frac{x_{n-\left(k+1\right)}}{1+{x}_n{x}_{n-1}\dots {x}_{n-k}},n=0,1,2,\dots $$where x−(k+1); x−k; : : : ; x−1; x0 ???? (0;∞) and k = 0; 1; 2; : : : . read more here.
Keywords: left right; right dots; recursive sequence; frac left ... See more keywords
Recursive sequence generation in crows
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DOI: 10.1126/sciadv.abq3356
Abstract: Recursion, the process of embedding structures within similar structures, is often considered a foundation of symbolic competence and a uniquely human capability. To understand its evolution, we can study the recursive aptitudes of nonhuman animals.… read more here.
Keywords: crows recursive; genealogy; generation crows; sequence generation ... See more keywords