This paper presents an enumeration algorithm to generate all magic squares of order 5 based on the
ideas of basic form (Schroeppel ) and generating vector which is extension of Frénicle Quads (Ollerenshaw
and Bondi ). The results lead us to extend Frénicle-Amela patterns from the case of order 4 to the case of
order 5, which we refer to Frénicle-Amela-Like patterns. We show that these interesting Frénicle-Amela-Like
patterns appear simultaneously. The number of these patterns is also calculated.
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Special Matrices is a peer-reviewed, open access electronic journal that publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences.