Floor-half generating function
= Floor-half generating function
The sequence $\lfloor n/2\rfloor$ has generating function
$$
\sum_{n\geq1}\left\lfloor\frac n2\right\rfloor x^n
=\frac{x^2}{(1-x)^2(1+x)}.
$$
= Floor-half generating function
The sequence $\lfloor n/2\rfloor$ has generating function
$$
\sum_{n\geq1}\left\lfloor\frac n2\right\rfloor x^n
=\frac{x^2}{(1-x)^2(1+x)}.
$$