  A new distribution for systems of particles obeying statistical exclusion of
correlated states is presented following the Haldane's state counting. It
relies upon a conjecture to deal with the multiple exclusion that takes place
when the states available to single particles are spatially correlated and it
can be simultaneously excluded by more than one particle. The Haldane's
statistics [F. D. M. Haldane, Phys. Rev. Lett. 67, 937 (1991)] and Wu's
distribution [Y.-S. Wu, Phys. Rev. Lett. 52, 2103 (1984)] are recovered in the
limit of non-correlated states (constant statistical exclusion) of the multiple
exclusion statistics. In addition, the exclusion spectrum function $G(n)$ is
introduced to account for the dependence of the statistical 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 simulations from
$k=2$ to $10$ where multiple exclusion dominates as $k$ increases.
