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In the present study, we have constructed new Banach sequence spaces  ℓ p L , c 0 L , c L , and  ℓ ∞ L , where  L = l v , k is a regular matrix defined by  l v , k = l k / l v + 2 − v + 2 ,   0 ≤ k ≤ v , 0 ,   k &gt; v , for all  v , k = 0 , 1 , 2 , ⋯ , where  l = l k is a sequence of Leonardo numbers. We study their topological and inclusion relations and construct Schauder bases of the sequence spaces  ℓ p L , c 0 L , and  c L . Besides,  α -,  β - and  γ -duals of the aforementioned spaces are computed. We state and prove results of the characterization of the matrix classes between the sequence spaces  ℓ p L , c 0 L , c L , and  ℓ ∞ L to any one of the spaces  ℓ 1 , c 0 , c , and  ℓ ∞ . Finally, under a definite functional  ρ and a weighted sequence of positive reals  r , we introduce new sequence spaces  c 0 L , r ρ and  ℓ p L , r ρ . We present some geometric and topological properties of these spaces, as well as the eigenvalue distribution of ideal mappings generated by these spaces and  s -numbers.

On New Banach Sequence Spaces Involving Leonardo Numbers and the Associated Mapping Ideal