#Challenge to Manuel Kauers and his computer (from DZ) #Consider the following 1838 by 1838 square matrix, M8, (with entries that are either 0 or powers of z) , #Compute the [1,2] entry of its ninth power. In Maple #evalm(M8&^9)[1,2] #(It is a polynomial in z of degree 64). In particular we are interested in one half of the coefficient of z^32 #I am offering to donate \$100 to the OEIS in your honor. This matrix was generated by my PhD student George Spahn #UPDATE: This challenge was met by Manuel Kauers. A donation has been made M8:= [[0, 0, 0, z, 0, z, 0, z, 0, z, 0, z, 0, z, 0, z, z, z^2, 0, 0, z^2, 0, 0, z^2, 0, 0, z^2, 0, 0, z^2, 0, 0, z^2, 0, z^2, 0, z^2, 0, 0, 0, 0, 0, 0, z^2, 0, 0, 0 , 0, 0, 0, z^2, 0, 0, 0, 0, 0, 0, z^2, 0, 0, 0, 0, 0, 0, z^2, 0, 0, z^2, 0, z^2 , 0, 0, 0, 0, 0, 0, z^2, 0, 0, 0, 0, 0, 0, z^2, 0, 0, 0, 0, 0, 0, z^2, 0, 0, z^ 2, 0, z^2, 0, 0, 0, 0, 0, 0, z^2, 0, 0, 0, 0, 0, 0, z^2, 0, 0, z^2, 0, z^2, 0, 0, 0, 0, 0, 0, z^2, 0, 0, z^2, 0, z^2, 0, 0, z^2, z^2, z^3, 0, 0, z^3, 0, 0, z^ 3, 0, 0, z^3, 0, 0, z^3, 0, z^3, 0, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, z^3, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0 , 0, z^3, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, 0, z^3, 0, 0 , 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^3, 0, 0, z^3, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, 0, z^3, 0, 0, 0, 0, 0, 0, z^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , z^3, 0, 0, z^3, 0, z^3, 0, 0, z^3, 0, 0, z^3, z^3, z^4, 0, 0, z^4, 0, 0, z^4, 0, 0, z^4, 0, z^4, 0, 0, z^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^4, 0, 0, 0, 0, 0, 0, z^4, 0, 0, z^4, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, z^4, 0, 0, 0, 0, 0, 0, z^4, 0, 0, z^4, 0, 0, 0, 0, 0, 0, z^4, 0, z^4, 0, 0, z^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^4, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, z^4, 0, 0, 0, 0, 0, 0, z^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^ 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, z^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^4, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^4, 0, 0, 0, 0, 0, 0, z^4, 0, 0, z^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^4, 0, 0, 0, 0, 0, 0, z ^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, z^4, 0, 0, 0, 0, 0, 0, z^4, 0 , 0, z^4, 0, 0, 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