This command returns the characteristic sequence of Fz as a function of Fn.

The characteristic generating function Cz of Fz is defined as:

The sequence encoded by Cz is the characteristic sequence of Fz.

The value FAIL is returned if Fz is a trivial rational generating function.

The command with(genfunc,rgf_charseq) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{genfunc}\right)\:$

$\mathrm{rgf\_charseq}\left(\frac{z}{1-z-z^2}\,z\,F\left(n\right)\,n\right)$

$F\left(n+1\right)$

$\mathrm{rgf\_charseq}\left(\frac{1+2z}{1-3z-4z^2}\,z\,t\left(n\right)\,n\right)$

$\frac{t\left(n\right)}{3}+\frac{4t\left(n-1\right)}{3}$

$\mathrm{Gy}≔\frac{1+y+y^2}{{\left(1-y\right)}^3}\:$

$\mathrm{rgf\_expand}\left(\mathrm{Gy}\,y\,j\right)$

$-3j-2+3\left(j+1\right)\left(\frac{j}{2}+1\right)$

$\mathrm{rgf\_charseq}\left(\mathrm{Gy}\,y\,\,j\right)$

$-j-\frac{5}{3}+\frac{8\left(j+1\right)\left(\frac{j}{2}+1\right)}{3}+\frac{\left(j-1\right)j}{3}-\frac{7j\left(\frac{j}{2}+\frac{1}{2}\right)}{3}$

$\mathrm{factor}\left(\right)$

$\frac{\left(j+2\right)\left(j+1\right)}{2}$

$\mathrm{rgf\_encode}\left(\,j\,z\right)$

$\frac{1}{1-z}+\frac{3z}{2{\left(1-z\right)}^2}+\frac{z\left(\frac{1}{{\left(1-z\right)}^2}+\frac{2z}{{\left(1-z\right)}^3}\right)}{2}$

$\mathrm{normal}\left(\right)$

$-\frac{1}{{\left(z-1\right)}^3}$