encode rational generating functions - Maple Help

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genfunc[rgf_encode] - encode rational generating functions

 Calling Sequence rgf_encode(Fn, n, z) rgf_encode(Fn, n, z, options)

Parameters

 Fn - closed form expression for the nth term in a sequence n - name, index variable for Fn z - name, generating function variable options - (optional) parameters defining special information about the sequence

Description

 • This function finds the rational generating function of the sequence defined by Fn.
 • The expression Fn must be a valid closed form expression for a sequence with a rational generating function. The command type(Fn, 'ratseq'(n)) will determine if Fn is a valid expression.
 • The sequence is assumed to be defined by Fn for all $0\le n$. The optional arguments can be used to specify other information about the sequence.
 An optional argument of the form $n=c$, where c is an integer value, defines the first nonzero term in the sequence to be at index c.
 An optional argument of the form $[\mathrm{i1}=\mathrm{v1},\mathrm{i2}=\mathrm{v2},...]$, where $\mathrm{i2},\mathrm{i2},\mathrm{...}$ are integer indices and $\mathrm{v1},\mathrm{v2},\mathrm{...}$ are values of the sequence at those indices.
 • The command with(genfunc,rgf_encode) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{genfunc}\right):$
 > $\mathrm{rgf_encode}\left({2}^{n},n,z\right)$
 $\frac{{1}}{{1}{-}{2}{}{z}}$ (1)
 > $\mathrm{rgf_encode}\left({2}^{k},k,y,k=2\right)$
 $\frac{{4}{}{{y}}^{{2}}}{{1}{-}{2}{}{y}}$ (2)
 > $\mathrm{rgf_encode}\left({2}^{n},n,z,\left[0=2,1=0\right]\right)$
 $\frac{{1}}{{1}{-}{2}{}{z}}{+}{1}{-}{2}{}{z}$ (3)