  In this note, we examine how the BKP structure of the generating series of
several models of maps on non-oriented surfaces can be used to obtain explicit
and/or efficient recurrence formulas for their enumeration according to the
genus and size parameters. Using techniques already known in the orientable
case (elimination of variables via Virasoro constraints or Tutte equations), we
naturally obtain recurrence formulas with non-polynomial coefficients. This
non-polynomiality reflects the presence of shifts of the charge parameter in
the BKP equation. Nevertheless, we show that it is possible to obtain
non-shifted versions, meaning pure ODEs for the associated generating
functions, from which recurrence relations with polynomial coefficients can be
extracted. We treat the cases of triangulations, general maps, and bipartite
maps. These recurrences with polynomial coefficients are conceptually
interesting but bigger to write than those with non-polynomial coefficients.
However they are relatively nice-looking in the case of one-face maps. In
particular we show that Ledoux's recurrence for non-oriented one-face maps can
be recovered in this way, and we obtain the analogous statement for the
(bivariate) bipartite case.
