Wolfram Language & System 11.0 (2016)|Legacy Documentation

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

yields terms nmin through nmax in the linear recurrence sequence.


  • 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}.
Introduced in 2008