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%I #7 Sep 25 2020 00:00:16
%S 1,1,1,10,20,64
%N a(n) is the number of essentially different n X n matrices with maximal sum of entries satisfying the conditions of A228882.
%C a(7) > 2630.
%H IBM Research, <a href="https://www.research.ibm.com/haifa/ponderthis/challenges/December2012.html">Maximal sum 6x6 grid</a>, Ponder This December 2012.
%H Hugo Pfoertner, <a href="/A337434/a337434.txt">List of solutions for n=5 and n=6</a>.
%e a(1) = 1: the 8 rotated and reflected matrices are equivalent
%e 1 1 1 1 1 2 1 3 2 3 3 2 2 1 3 1
%e 2 3 3 2 1 3 1 2 1 1 1 1 3 1 2 1
%e .
%e a(3) = 1: due to mirror symmetry, there are only 4 equivalent matrices
%e 2 4 1 1 4 2 1 2 1 2 1 2
%e 1 3 2 2 3 1 4 3 4 4 3 4
%e 2 4 1 1 4 2 2 1 2 1 2 1
%e .
%e a(4) = 10:
%e 2 1 2 3 2 1 2 3 2 1 2 3 2 1 2 3 2 1 2 3
%e 3 4 2 1 3 4 5 1 3 4 5 1 3 5 2 1 3 5 4 1
%e 1 5 3 4 1 2 3 4 1 2 3 4 1 4 3 4 1 2 3 4
%e 3 2 1 2 2 3 1 2 3 2 1 2 3 2 1 2 2 3 1 2
%e .
%e 2 1 2 3 2 1 2 3 2 1 2 3 3 1 2 3 3 1 2 3
%e 3 5 4 1 4 3 4 1 4 3 5 1 2 3 3 1 2 3 3 1
%e 1 2 3 4 1 2 5 3 1 2 4 3 1 4 5 2 1 5 4 2
%e 3 2 1 2 2 3 1 2 2 3 1 2 3 2 1 3 3 2 1 3
%Y Cf. A228882.
%K nonn,hard,more
%O 1,4
%A _Hugo Pfoertner_, Sep 22 2020