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recurrence relation
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recurrence relation

mathematics
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A recurrence relation is a formula that defines a sequence where each term is determined by preceding terms. For example, if fn represents a term in a sequence, a recurrence relation expresses fn + k as a linear combination of earlier terms. These relations, along with initial values, uniquely define the entire sequence.12

An example is the relation fn = fn-1 + fn-2, which, with initial values like f0 = 1 and f1 = 2, generates the sequence 1, 2, 3, 5, 8, and so on. This type of relation is fundamental in combinatorics for solving enumeration problems.2

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2 Britannica Sources
  1. recurrence formula
  2. combinatorics - Recurrence relations and generating functions

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