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In mathematics, a sequence *a* = (*a*_{0}, *a*_{1}, ..., *a*_{n}) of nonnegative real numbers is called a **logarithmically concave sequence**, or a **log-concave sequence** for short, if *a*_{i}^{2} ≥ *a*_{i−1}*a*_{i+1} holds for 0 < *i* < *n* .

*Remark:* some authors (explicitly or not) add two further conditions in the definition of log-concave sequences:

*a*is non-negative*a*has no internal zeros; in other words, the support of*a*is an interval of**Z**.

These conditions mirror the ones required for log-concave functions.

Sequences that fulfill the three conditions are also called **Pólya Frequency sequences of order 2** (**PF _{2}** sequences). Refer to chapter 2 of

Examples of log-concave sequences are given by the binomial coefficients along any row of Pascal's triangle and the elementary symmetric means of a finite sequence of real numbers.

**^**Brenti, Francesco (1989).*Unimodal, log-concave and Pólya frequency sequences in combinatorics*. Providence, R.I.: American Mathematical Society. ISBN 978-1-4704-0836-7. OCLC 851087212.

- Stanley, R. P. (December 1989). "Log-Concave and Unimodal Sequences in Algebra, Combinatorics, and Geometry".
*Annals of the New York Academy of Sciences*.**576**: 500–535. doi:10.1111/j.1749-6632.1989.tb16434.x.