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The first argument should be a single recurrence relation or a set of recurrence relations. Any expressions in eqns which are not equations will be understood to be equal to zero.

The second argument fcns indicates the functions from eqns over which they are considered to be recurrences. The names must always be entered in the form function(var).

The third argument inits is a set of initial conditions on the functions fcns.

The result of an REcreate call is an RESol data-structure, which is much easier to handle than a raw recurrence equation.

In the rest of this package, a problem is synonymous with either valid input for REcreate or a valid RESol data structure.

$\mathrm{LREtools}\left[\mathrm{REcreate}\right]\left(\left(18+12n\right)t\left(n\right)+\left(-20-7n\right)t\left(n+1\right)+\left(4+n\right)t\left(n+2\right)\,t\left(n\right)\,\left\{t\left(0\right)=0\,t\left(1\right)=2\right\}\right)$

$\mathrm{RESol}\left(\left\{\left(18+12n\right)t\left(n\right)+\left(-20-7n\right)t\left(n+1\right)+\left(4+n\right)t\left(n+2\right)=0\right\}\,\left\{t\left(n\right)\right\}\,\left\{t\left(0\right)=0\,t\left(1\right)=2\right\}\,\mathrm{INFO}\right)$

$\mathrm{rec}≔a\left(n+2\right)-\frac{\left(2n+1\right)a\left(n+1\right)}{n}+\frac{na\left(n\right)}{n-1}=n\left(n+1\right)\:$

$\mathrm{LREtools}\left[\mathrm{REcreate}\right]\left(\mathrm{rec}\,a\left(n\right)\,\varnothing \right)$

$\mathrm{RESol}\left(\left\{n^{2}a\left(n\right)+\left(-2n^2+n+1\right)a\left(n+1\right)+\left(n^2-n\right)a\left(n+2\right)=n^2\left(n-1\right)\left(n+1\right)\right\}\,\left\{a\left(n\right)\right\}\,\left\{a\left(1\right)=0\,a\left(2\right)=a\left(2\right)\,a\left(3\right)=a\left(3\right)\right\}\,\mathrm{INFO}\right)$