Is there direct notation for this sum

Question

for this boy here I don't know how to deal with the dependence to the outer sum or the floor $$f(x)=2+\sum_{i=0}^{x-1}\left(4+1+\sum_{j=1}^{\lfloor\frac{x-1}{2}\rfloor}(2+1)+1\right)+3$$

Answer 1

Note that $\sum_{k=a}^b c=(b-a+1)c$ (perhaps only under the premise that $b\ge a-1$). Thus $$ \sum_{j=1}^{\lfloor \frac{x-1}2\rfloor}(2+1)=3\cdot\left\lfloor \frac{x-1}2\right\rfloor$$ and $$\begin{align}f(x)&=5+x\cdot\left(6+3\cdot\left\lfloor \frac{x-1}2\right\rfloor\right) \\&=5+6x+3x\left\lfloor \frac{x-1}2\right\rfloor\\ &=\begin{cases}\frac32x^2+\frac92x+5&\text{if $x$ is odd}\\ \frac32x^2+3x+5&\text{if $x$ is even.}\end{cases}\end{align}$$