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The sequence $G(2n,2k)$ is $T(n,k)/2$, where $T(n,k)$ is A051601. For $G(2n,2k+1)$ boundary conditions $1,3,5,7,\ldots$ can be replaced by $0,2,4,6$ (minus one Pascal triangle). It gives $G(2n,2k)$ ag …

Suppose we know that $y_j=x_j^2$ for $j=n-1, \ldots, n-k$. Then $$x_n^2=\left(\frac{x_{n-1}^2+x_{n-2}^2+\cdots+x_{n-k+1}^2}{x_{n-k}} \right)^2=\frac{(y_{n-1}+y_{n-2}+\cdots+y_{n-k+1})^2}{y_{n-k}} =y_n …

This question is motivated by integrability of the sequence mistakenly arisen in the question Does this sequence always give an integer? Let $m_1,\ldots, m_{k-1}$ be positive integers and sequence $\ …

This graph is looks like a graf of the function which replaces partial quotient (in nearest integer continued fraction) in the following way: $$a_i+~\leftrightarrow~a_i+1-.$$ For example $$0+\cfrac{1} …

Elliptic Curve Digital Signature Algorithm (ECDSA) admits universal forgery (UF) if the Attacker can solve the equation $$z=\frac{f_{k-1}(x,y)f_{k+1}(x,y)}{f_{k}(x,y)^2},$$ where $k$ is unknown, $f_{k …