  A new distribution for systems of particles in equilibrium obeying exclusion
of correlated states is presented following the Haldane's state counting. It
relies upon an ansatz to deal with the multiple exclusion that takes place when
the states accessible to single particles are spatially correlated and it can
be simultaneously excluded by more than one particle. The Haldane's statistics
and Wu's distribution are recovered in the limit of non-correlated states of
the multiple exclusion statistics. In addition, an exclusion spectrum function
$\mathcal{G}(n)$ is introduced to account for the dependence of the state
exclusion on the occupation-number $n$. Results of thermodynamics and state
occupation are shown for ideal lattice gases of linear particles of size $k$
($k$-mers) where multiple exclusion occurs. Remarkable agreement is found with
Grand-Canonical Monte Carlo simulations from $k$=2 to 10 where multiple
exclusion dominates as $k$ increases.
