New posts in Recurrence Relations

Is there more to this relationship with the Fibonacci numbers?

If $u_1=1$ and $u_{n+1} = n+\sum_{k=1}^n u_k^2$, then $u_n$ is never a square.

How to write $[(2+\sqrt{3})^n + (2-\sqrt{3})^n + (2+\sqrt{3})^{n+1} + (2-\sqrt{3})^{n+1}]/6$ to the form $a^2 + 2 b^2$ ($a, b \in \mathbb{N}$).

finding a solution for this recurrence relation

Do you know any research on finding closed forms of recursively-defined sequences?

Closed form of recurrent arithmetic series summation

Stirling numbers of second kind, but no two adjacent numbers in same part.

Why does this iterative way of solving an equation work?

Prove that $x_n$ and $n$ are coprimes

Is there a closed form for the recurrence $V_{n+1}={V_n+\Delta V\over 1+{V_n\cdot \Delta V/C^2}}$, for constants $\Delta V$ and $C$?