Mathematica: Given a first row with even valued length n construct a matrix which is both symmetr...

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Given a first row with even valued length n construct a matrix which is both symmetric and persymmetric
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(mathematica.stackexchange.com/users/94691/phillip-dukes)Phillip Dukes
(mathematica.stackexchange.com/users/72953/ydd)ydd
(mathematica.stackexchange.com/users/84894/lericr)lericr
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