# LinearRecurrence

LinearRecurrence[ker,init,n]

gives the sequence of length n obtained by iterating the linear recurrence with kernel ker starting with initial values init.

LinearRecurrence[ker,init,{n}]

gives the n term.

LinearRecurrence[ker,init,{nmin,nmax}]

yields terms nmin through nmax.

# Details

• The ker and init can involve arbitrary symbolic expressions, as well as arrays.
• The initial list init must be at least as long as the kernel list ker.
• If init is longer than ker, only the last Length[ker] elements are used.
• LinearRecurrence[{a1,,ad},{y1,,yd},n] iterates the recurrence equation with initial conditions , , .
• When coefficients ai and initial values yj are arrays, then the iterated recurrence is interpreted as with dot products of coefficient and values.
• If the initial values yj have dimensions {m1,,ms} then the coefficients ai must either be scalar or must have dimensions {m1,m1}.

# Examples

open allclose all

## Basic Examples(3)

 In[1]:=
 Out[1]=

Solve an initial-value problem for a first-order difference equation with kernel {-3, 1}:

 In[1]:=
 Out[1]=

Find the first few Fibonacci numbers:

 In[1]:=
 Out[1]=
 In[2]:=
 Out[2]=