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We develop the basis of the two dimensional generalized quantum statisticalsystems by using results on $r$-generalized Fibonacci sequences. According tothe spin value $s$ of the 2d-quasiparticles, we distinguish four classes ofquantum 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 quasiparticleswith $s=1/M:mod(1)$, $M\geq 2,$, we show that the statistical weights densities$\rho_M$ are given by the integer hierarchies of Fibonacci sequences. This is aremarkable result which envelopes naturally the Fermi and Bose statistics andmay be thought of as an alternative way to the Haldane interpolatingstatistical method.Comment: Late

FRACTIONAL STATISTICS IN TERMS OF THE r-GENERALIZED FIBONACCI SEQUENCES