After reviewing the group structure and representation theory for dihedral $$D_{2n},$$ we consider an intertwining operator $$\varPhi _\rho $$ from algebra $$\mathbb {C}[D_{2n}]$$ into a corresponding space of semi-magic matrices. From this operator, one obtains generating function enumerating associated squares with fixed line sum extending circulant While work complements approach to $$D_{2n}...
