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

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

Offset

3,1

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

Links

Table of n, a(n) for n=3..9.

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

Example

(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.

Crossrefs

Cf. A201126 (water retention of magic squares).

Sequence in context: A052149 A062966 A347722 * A259709 A078155 A237530

Adjacent sequences: A201124 A201125 A201126 * A201128 A201129 A201130

Keyword

nonn,hard,nice,more

Author

Hugo Pfoertner, Dec 03 2011

Status

approved