  We address the issue of constraining the class of $f(\mathcal{R})$ able to
reproduce the observed cosmological acceleration, by using the so called
cosmography of the universe. We consider a model independent procedure to build
up a $f(z)$-series in terms of the measurable cosmographic coefficients; we
therefore derive cosmological late time bounds on $f(z)$ and its derivatives up
to the fourth order, by fitting the luminosity distance directly in terms of
such coefficients. We perform a Monte Carlo analysis, by using three different
statistical sets of cosmographic coefficients, in which the only assumptions
are the validity of the cosmological principle and that the class of
$f(\mathcal{R})$ reduces to $\Lambda$CDM when $z\ll1$. We use the updated union
2.1 for supernovae Ia, the constrain on the $H_0$ value imposed by the
measurements of the Hubble space telescope and the Hubble dataset, with
measures of $H$ at different $z$. We find a statistical good agreement of the
$f(\mathcal{R})$ class under exam, with the cosmological data; we thus propose
a candidate of $f(\mathcal{R})$, which is able to pass our cosmological test,
reproducing the late time acceleration in agreement with observations.
