  We first recall Solomon's relations for Welschinger's invariants counting
real curves in real symplectic fourfolds, announced in \cite{Jake2} and
established in \cite{RealWDVV}, and the WDVV-style relations for Welschinger's
invariants counting real curves in real symplectic sixfolds with some symmetry
established in \cite{RealWDVV3}. We then explicitly demonstrate that in some
important cases (projective spaces with standard conjugations, real blowups of
the projective plane, and two- and three-fold products of the one-dimensional
projective space with two involutions each), these relations provide complete
recursions determining all Welschinger's invariants from basic input. We
include extensive tables of Welschinger's invariants in low degrees obtained
from these recursions with {\it Mathematica}. These invariants provide lower
bounds for counts of real rational curves, including with curve insertions in
smooth algebraic threefolds.
