A Generalization of the $k$-Bonacci Sequence from Riordan Arrays

[摘要] In this article, we introduce  a family of weighted lattice paths, whose step set is $\{H=(1,0), V=(0,1), D_1=(1,1), \dots, D_{m-1}=(1,m-1)\}$. Using these lattice paths, we define a family of Riordan arrays whose sum on the rising diagonal is the $k$-bon

[学科分类] 离散数学和组合数学

[关键词] Riordan arrays;$k$-bonacci sequence;lattice paths