Combinatorial Interpretation of Numbers in the Generalized Padovan Sequence and Some of Its Extensions Article Swipe

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Fibonacci number Generalization Combinatorial principles Sequence (biology) Interpretation (philosophy) Combinatorial analysis Mathematics Combinatorics Combinatorial explosion Computer science Discrete mathematics Programming language Mathematical analysis Biology Genetics

Renata Passos Machado Vieira , Francisco Régis Vieira Alves , Paula Catarino ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.3390/axioms11110598 · OA: W4307948214

There is ongoing research into combinatorial methods and approaches for linear and recurrent sequences. Using the notion of a board defined for the Fibonacci sequence, this work introduces the Padovan sequence combinatorial approach. Thus, mathematical theorems are introduced that refer to the study of the Padovan combinatorial model and some of its extensions, namely Tridovan, Tetradovan and its generalization (Z-dovan). Finally, we obtained a generalization of the Padovan combinatorial model, which was the main result of this research.