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A linear recurrence relation is an equation that expresses each element of a sequence as a linear function of the preceding ones. More precisely, in the case where only the immediately preceding element is involved, a linear recurrence relation has the form where
is a everywhere defined function that involves consecutive elements of the sequence. In this case, initial values are needed for defining a sequence.
Taking into account that is defined only for equals to the powers of 2, and hence is not defined for the rest natural numbers, the previous definition implies that is not a linear recurrence relation.