Geodesic
Linear recurrent relations, power series distributions, and generalized allocation scheme
Diskretnaya Matematika, Tome 32 (2020) no. 3, pp. 98-112.

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We consider distributions of the power series type determined by the generating functions of sequences satisfying linear recurrence relations with nonnegative coefficients. These functions are represented by power series with positive radius of convergence. An integral limit theorem is proved on the convergence of such distributions to the exponential distribution. For the generalized allocation scheme generated by these linear relations a local normal theorem for the total number of components is proved. As a consequence of more general results of the author, a limit theorem is stated containing sufficient conditions under which the distributions of the number of components having a given volume converge to the Poisson distribution.
Keywords: generalized allocation scheme, power series distribution, linear recurrence relations, characteristic functions, Fibonacci numbers, saddle-point method. 
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A. N. Timashev. Linear recurrent relations, power series distributions, and generalized allocation scheme. Diskretnaya Matematika, Tome 32 (2020) no. 3, pp. 98-112. http://geodesic.mathdoc.fr/item/DM_2020_32_3_a7/

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