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A201127 Maximum water retention of a semi-magic square of order n.

%I A201127 #33 Mar 12 2022 22:43:43
%S A201127 4,22,78,199,424,814,1410
%N A201127 Maximum water retention of a semi-magic square of order n.
%C A201127 The same rules as for A201126 apply, but with the magic conditions for both diagonals of the number square removed.
%C A201127 a(10) >= 2280. - _Hugo Pfoertner_, May 19 2012
%H A201127 Hugo Pfoertner, <a href="/A201127/a201127.png">3 X 3 Semi-magic square retaining 4 units of water</a>
%H A201127 Hugo Pfoertner, <a href="/A201127/a201127_1.png">4 X 4 Semi-magic square retaining 22 units of water</a>
%H A201127 Walter Trump, <a href="/A201127/a201127_7.png">5 X 5 Semi-magic square retaining 78 units of water</a>
%H A201127 Hugo Pfoertner, <a href="/A201127/a201127_3.png">6 X 6 Semi-magic square retaining 199 units of water</a>
%H A201127 Hugo Pfoertner, <a href="/A201127/a201127_4.png">7 X 7 Semi-magic square retaining 424 units of water</a>
%H A201127 Hugo Pfoertner, <a href="/A201127/a201127_5.png">8 X 8 Semi-magic square retaining 814 units of water</a>
%H A201127 Hugo Pfoertner, <a href="/A201127/a201127_6.png">9 X 9 Semi-magic square retaining 1410 units of water</a>
%H A201127 Wikipedia, <a href="http://en.wikipedia.org/wiki/Water_retention_on_mathematical_surfaces">Water retention on mathematical surfaces</a>
%e A201127 (7 6 2)
%e A201127 (5 1 9)
%e A201127 (3 8 4)
%e A201127 is a semi-magic square. The mid-side bricks with heights 6, 5, 9, 8 form a wall around the central hole with bottom height 1. Water poured upon the square will fill the central pond until overflowing via the left brick of height 5. Thus 4 units of water will be retained.
%Y A201127 Cf. A201126 (water retention of magic squares).
%K A201127 nonn,hard,nice,more
%O A201127 3,1
%A A201127 _Hugo Pfoertner_, Dec 03 2011