New posts in Recurrence Relations

Given a recursion $a_{n+ 1}= \sqrt{na_{n}+ 2n+ 1}$ with $a_{1}\geq 1.$ Prove that $a_{n}\sim n\,{\rm as}\,n\rightarrow\infty$

Finding the value of $ax^4+by^4$

Is there a closed form for this recursion equation?

Given $f(i, j) = f(i − 1, j − 1) + f(i, j − 1)$, find the value of $f(1009, 2019)$

What is the sign of the integral $\int_{0}^{2\pi}e^{\sin(x)}\cos(nx)\,dx$?

Number of ways to represent any N as sum of odd numbers?

A unique question in combinatorics and non-commutative variables.

Finding the the number of Lattice paths with three steps.

Behaviour of $u_{n}=u_{\lfloor n/2\rfloor}+u_{\lfloor n/3\rfloor}+u_{\lfloor n/6\rfloor}$

Suppose each $x_{n+1} \le \left(\sum_{i=1}^n x_i \right)^{-c}$ for some $c \in (0,1)$. How quickly can $\sum_{i=1}^n x_i $ grow?