Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.View current documentation (Version 11.2)


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

yields terms through 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 and initial values are arrays, then the iterated recurrence is interpreted as with dot products of coefficient and values.
  • If the initial values have dimensions then the coefficients must either be scalar or must have dimensions .
Introduced in 2008