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A201127 Maximum water retention of a semi-magic square of order n. 2
4, 22, 78, 199, 424, 814, 1410 (list; graph; refs; listen; history; text; internal format)



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


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

Hugo Pfoertner, 3X3 Semi-magic square retaining 4 units of water

Hugo Pfoertner, 4X4 Semi-magic square retaining 22 units of water

Walter Trump, 5X5 Semi-magic square retaining 78 units of water

Hugo Pfoertner, 6X6 Semi-magic square retaining 199 units of water

Hugo Pfoertner, 7X7 Semi-magic square retaining 424 units of water

Hugo Pfoertner, 8X8 Semi-magic square retaining 814 units of water

Hugo Pfoertner, 9X9 Semi-magic square retaining 1410 units of water

Wikipedia, Water retention on mathematical surfaces


(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.


Cf. A201126 (water retention of magic squares).

Sequence in context: A241689 A052149 A062966 * A078155 A237530 A096167

Adjacent sequences:  A201124 A201125 A201126 * A201128 A201129 A201130




Hugo Pfoertner, Dec 03 2011



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Last modified December 20 17:17 EST 2014. Contains 252270 sequences.