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 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 .
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