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

4, 22, 78, 199, 424, 814, 1410

Offset: 3

Author

Hugo Pfoertner, Dec 03 2011

Keywords

• nonn
• hard
• nice
• more

Comments

The same rules as for A201126 apply, but with the magic conditions for both diagonals of the number square removed.

a(10) >= 2280. - Hugo Pfoertner, May 19 2012

Examples

			(7 6 2)
(5 1 9)
(3 8 4)
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.
		

Links

• Hugo Pfoertner, 3 X 3 Semi-magic square retaining 4 units of water
• Hugo Pfoertner, 4 X 4 Semi-magic square retaining 22 units of water
• Walter Trump, 5 X 5 Semi-magic square retaining 78 units of water
• Hugo Pfoertner, 6 X 6 Semi-magic square retaining 199 units of water
• Hugo Pfoertner, 7 X 7 Semi-magic square retaining 424 units of water
• Hugo Pfoertner, 8 X 8 Semi-magic square retaining 814 units of water
• Hugo Pfoertner, 9 X 9 Semi-magic square retaining 1410 units of water
• Wikipedia, Water retention on mathematical surfaces

Crossrefs

Cf. A201126 (water retention of magic squares).