4 problems

Let $F_m$ be the set of periodic sequences from the Fibonacci recurrence or its parity transform with initial condition $(a_0,a_1)\in(\mathbb Z/m\mathbb Z)^2$, taken modulo $m$. Fo…

Let $p$ be prime, and let $\#(p)$ count distinct periods modulo $p$ of the Fibonacci recurrence and its parity transform over all initial conditions…

Period Count for $x^n-1$.

Let $\vec{b}=(1^2,3^2,5^2,\dots)$, and let $C_n^{\vec{b}}$ denote the corresponding weighted Catalan number, which counts combinatorial types of Morse links of order $n$. For a pos…