Enumerative combinatorics
Generating functionology
Generating functions for generating trees
Discrete Mathematics
Kernel method and system of functional equations
Journal of Computational and Applied Mathematics
The kernel method and systems of functional equations with several conditions
Journal of Computational and Applied Mathematics
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In this paper we solve several recurrence relations with two (three) indices using combinatorial methods. Moreover, we present several recurrence relations with two (three) indices related to ternary paths and k-ary paths.