  In this paper we study odd unimodal and odd strongly unimodal sequences. We
use $q$-series methods to find several fundamental generating functions.
Employing the Euler--Maclaurin summation formula we obtain the asymptotic main
term for both types of sequences. We also find families of congruences modulo
$4$ for the number of odd strongly unimodal sequences.

Number Theory;Combinatorics