# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# 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,{nmin,nmax}]
yields terms nmin through nmax in the linear recurrence sequence.

## DetailsDetails

• 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}.

## ExamplesExamplesopen allclose all

### Basic Examples  (3)Basic Examples  (3)

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

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Find the first few Fibonacci numbers:

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