Petro, Kolosov

In this paper described numerical expansion of natural-valued power function $x^n$, in point $x=x_0$ where $(n, \ x_0)$ - natural numbers. Applying numerical methods, that is calculus of finite differences, namely, discrete case of Binomial expansion is reached. Received results were compared with solutions according to Newtonâ€™s Binomial theorem an...

Petro, Kolosov

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence $\href{https://oeis.org/A287326}{A287326}$ in OEIS. The main property of $\href{https://oeis.org/A287326}{A287326}$ that it returns a perfect cube $n$ as sum of $n$-th row terms over $k, \ 0\leq k\leq n-1$ or $1\leq k\leq n$, by means of its symm...

Kolosov, Petro

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence $\href{https://oeis.org/A287326}{\mathrm{A287326}}$ in OEIS. The main property of $\href{https://oeis.org/A287326}{\mathrm{A287326}}$ that it returns a perfect cube $n$ as sum of $n$-th row terms over $k, \ 0\leq k\leq n-1$ or $1\leq k\leq n$, by...

Petro, Kolosov

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence $\href{https://oeis.org/A287326}{A287326}$ in OEIS. The main property of $\href{https://oeis.org/A287326}{A287326}$ that it returns a perfect cube $n$ as sum of $n$-th row terms over $k, \ 0\leq k\leq n-1$ or $1\leq k\leq n$, by means of its symm...

Petro, Kolosov

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence $\href{https://oeis.org/A287326}{A287326}$ in OEIS. The main property of $\href{https://oeis.org/A287326}{A287326}$ that it returns a perfect cube $n$ as sum of $n$-th row terms over $k, \ 0\leq k\leq n-1$ or $1\leq k\leq n$, by means of its symm...

Petro, Kolosov

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence $\href{https://oeis.org/A287326}{A287326}$ in OEIS. The main property of $\href{https://oeis.org/A287326}{A287326}$ that it returns a perfect cube $n$ as sum of $n$-th row terms over $k, \ 0\leq k\leq n-1$ or $1\leq k\leq n$, by means of its symm...

Petro, Kolosov

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence $\href{https://oeis.org/A287326}{A287326}$ in OEIS. The main property of $\href{https://oeis.org/A287326}{A287326}$ that it returns a perfect cube $n$ as sum of $n$-th row terms over $k, \ 0\leq k\leq n-1$ or $1\leq k\leq n$, by means of its symm...

Emme, Jordan Prikhod'ko, Alexander

Let $s_2(x)$ denote the number of digits ``$1$'' in a binary expansion of any $x \in \mathbb{N}$. We study the mean distribution $\mu_a$ of the quantity $s_2(x+a)-s_2(x)$ for a fixed positive integer $a$.It is shown that solutions of the equation$$ s_2(x+a)-s_2(x)= d $$are uniquely identified by a finite set of prefixes in $\{0,1\}^*$, and that the...

Emme, Jordan Prikhod'ko, Alexander

Let $s_2(x)$ denote the number of digits ``$1$'' in a binary expansion of any $x \in \mathbb{N}$. We study the mean distribution $\mu_a$ of the quantity $s_2(x+a)-s_2(x)$ for a fixed positive integer $a$.It is shown that solutions of the equation$$ s_2(x+a)-s_2(x)= d $$are uniquely identified by a finite set of prefixes in $\{0,1\}^*$, and that the...

Emme, Jordan Prikhod'ko, Alexander

Let $s_2(x)$ denote the number of digits ``$1$'' in a binary expansion of any $x \in \mathbb{N}$. We study the mean distribution $\mu_a$ of the quantity $s_2(x+a)-s_2(x)$ for a fixed positive integer $a$.It is shown that solutions of the equation$$ s_2(x+a)-s_2(x)= d $$are uniquely identified by a finite set of prefixes in $\{0,1\}^*$, and that the...