The complex-type Padovan$-p$ sequences
Mathematica Moravica, Tome 26 (2022) no. 1.

Voir la notice de l'article dans eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this paper, we define the complex-type Padovan-$p$ sequence and then give the relationships between the Padovan-$p$ numbers and the complex-type Padovan-$p$ numbers. Also, we provide a new Binet formula and a new combinatorial representation of the complex-type Padovan-$p$ numbers by the aid of the $n$th power of the generating matrix of the complex-type Padovan-$p$ sequence. In addition, we derive various properties of the complex-type Padovan-$p$ numbers such as the permanental, determinantal and exponential representations and the finite sums by matrix methods.
Mots-clés : The complex-type Padovan-$p$ sequence, matrix, representation. 
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Özgür Erdağ; Serpil Halıcı; Ömür Deveci. The complex-type Padovan$-p$ sequences. Mathematica Moravica, Tome 26 (2022) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2022_26_1_a5/