OFFSET
2,1
COMMENTS
A magic square of order 2n is most-perfect if the following two conditions hold: (i) every 2 x 2 subsquare (including wrap-around) sum to 2T; and (ii) any pair of elements at distance n along a diagonal or a skew diagonal sum to T, where T= S/n, S is the magic constant.
All most-perfect magic squares are pandiagonal.
All pandiagonal magic squares of order 4 are most-perfect (cf. A191533).
LINKS
N. Makarova, Puzzle 671: Most Perfect Magic Squares, Prime Puzzles & Problems.
Wikipedia, Most-perfect magic square
EXAMPLE
a(3)=29790 corresponds to the following most-perfect magic square of order 6:
149 9161 2309 6701 2609 8861
9067 1483 6907 3943 6607 1783
4139 5171 6299 2711 6599 4871
3229 7321 1069 9781 769 7621
5987 3323 8147 863 8447 3023
7219 3331 5059 5791 4759 3631
a(4)=24024 corresponds to the following most-perfect magic square of order 8:
19 5923 1019 4423 4793 1277 3793 2777
4877 1193 3877 2693 103 5839 1103 4339
499 5443 1499 3943 5273 797 4273 2297
5297 773 4297 2273 523 5419 1523 3919
1213 4729 2213 3229 5987 83 4987 1583
5903 167 4903 1667 1129 4813 2129 3313
733 5209 1733 3709 5507 563 4507 2063
5483 587 4483 2087 709 5233 1709 3733
CROSSREFS
KEYWORD
bref,nonn,more
AUTHOR
Natalia Makarova, May 23 2015
STATUS
approved