  We develop the basis of the two dimensional generalized quantum statistical
systems by using results on $r$-generalized Fibonacci sequences. According to
the spin value $s$ of the 2d-quasiparticles, we distinguish four classes of
quantum statistical systems indexed by $ s=0,1/2:mod(1)$, $s=1/M:mod(1)$,
$s=n/M:mod(1)$ and $0\leq s\leq 1:mod(1)$. For quantum gases of quasiparticles
with $s=1/M:mod(1)$, $M\geq 2,$, we show that the statistical weights densities
$\rho_M$ are given by the integer hierarchies of Fibonacci sequences. This is a
remarkable result which envelopes naturally the Fermi and Bose statistics and
may be thought of as an alternative way to the Haldane interpolating
statistical method.
