Quasipolynomial

• assume $a_n = \left((-1)^n+1\right)+\left((-1)^n+3\right) n$
• then

$$ \sum_{n=0}^{\infty}a_nt^n = \frac{2 \left(t^3+3 t^2+t+1\right)}{(1-t)^2 (t+1)^2} $$

prop

Let $f$ be a quasipolynomial of degree $d$. If $f(n+1)\geq f(n)$ for all $n\in \mathbb{N}$, then the top degree coefficient of $f$ must be constant.