A337434 - OEIS

%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