See also section 5.14.2
The rsolve command takes three arguments; an equation or
list of equations that define a recurrence relation, the functions
(with their variables) used, and equations for the starting values.
For example, if a recurrence relation is defined by un+1 =
f(un,n) with u0 = a, the arguments to rsolve will be
u(n+1) = f(u(n),n), u(n) and
u(0)=a. The recurrence relation must either be a homogeneous
linear part with a nonhomogeneous part being a linear combination of
polynomials in n times geometric terms in n (such as
un+1 = 2 un + n 3n), or a
linear fractional transformation (such as un+1 =
(un−1)/(un−2)).
rsolve returns a matrix whose rows are the values of the
sequence as functions of n.
Note that rsolve is more flexible than seqsolve since:
Examples: