Hyper-Leonardo p-numbers and associated norms

In this paper, we introduce hyper-Leonardo p-numbers, which generalize "hyper-Leonardo numbers".We establish their various combinatorial properties, including recurrence relations, summation formulas, and the generating function.We also compute Euclidean norms and obtain bounds for spectral norms of different forms of k-circulant matrices associated with hyper-Leonardo p-numbers.Additionally, we derive some bounds for spectral norms of Kronecker and Hadamard products involving these matrices.