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Ordinary generating function of a recurrence

For a sequence

(u_{n})

, the ordinary generating function is

G (x) = \sum_{n \geq 0} u_{n} x^{n} .

Multiplying a linear recurrence by

x^{n}

and summing converts shifts of the sequence into polynomial multiples of

G

.

Table of contents 41 1
- Floor-half generating function Ordinary generating function of a recurrence 11

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