초록
Let ${\alpha}$ = (${\alpha}_1,\;{\alpha}_2$,...) and ${\beta}$ = (${\beta}_1,\;{\beta}_2$,...) be two sequences with ${\alpha}_1$ = ${\beta}_1$ and k and n be natural numbers. We denote by $A^{(k,{\pm})}_{{\alpha},{\beta}}(n)$ the matrix of order n with coefficients ${\alpha}_{i,j}$ by setting ${\alpha}_{1,i}$ = ${\alpha}_i,\;{\alpha}_{i,1}$ = ${\beta}_i$ for 1 ${\leq}$ i ${\leq}$ n and $${\alpha}_{i,j}=\{{\alpha}_{i-1,j-1}+{\alpha}_{i-1,j}\;if\;j{\equiv}$$2,3,4,..., k + 1 (mod 2k) $$\{{\alpha}_{i-1,j-1}-{\alpha}_{i-1,j}\;if\;j{\equiv}$$ k + 2,..., 2k + 1 (mod 2k) for 2 ${\leq}$ i, j ${\leq}$ n. The aim of this paper is to study the determinants of such matrices related to certain sequence ${\alpha}$ and ${\beta}$ and some natural numbers k.