| Abstract [eng] |
In this Master’s thesis, convolution-type recursive sequences a} defined by a given sequence b are investigated. The main objective of the thesis is to analyze the structure of such sequences, derive explicit expressions for their terms, and determine conditions under which the limits of the sequences exist. In the theoretical part, auxiliary sequences are introduced, allowing each term of the studied sequence to be expressed as a linear combination of the initial values, and generating function methods are employed to examine the behavior of the sequences. Concrete examples are provided to demonstrate how the theoretical results apply to different choices of the sequence b and to reveal the diverse behavior of the considered recursive sequences. |
