login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A050257 Number of distinct antimagic squares of order n (modulo rotations and reflections). 4
0, 0, 0, 299710 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
An Anti-Magic Square (AMS) is an arrangement of the numbers 1 to n*n in a square matrix such that the row, column and diagonal sums form a sequence of consecutive integers.
Cormie et al. estimated that the total number of 5 X 5 antimagic squares is on the order of 10^17. However, computational evidence suggests that the number of such squares is on the order of 10^15. Out of 19 billion randomly generated 5 X 5 matrices with distinct entries in {1, 2, ..., 25}, only 6 formed antimagic squares (see Examples below). - John M. Campbell, Nov 27 2022
REFERENCES
J. Cormie, V. Linek, S. Jiang, and R.-C. Chen, Investigating the antimagic square, J. Combin. Math. Combin. Comput., 43 (2002), 175-197.
LINKS
J. Cormie, Example: sorting the sums (numbers in black on the border) yields the sequence: 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269 (from web page above).
Eric Weisstein's World of Mathematics, Antimagic Square.
EXAMPLE
The following are antimagic squares of order 5.
[22 7 20 1 18] [ 2 22 11 6 21]
[ 5 2 25 15 17] [ 3 24 15 8 20]
[13 19 6 24 3] [12 19 14 16 7]
[11 8 14 21 12] [18 1 9 23 13]
[16 23 4 9 10] [25 5 17 10 4]
.
[ 3 12 18 21 17] [13 12 19 4 18]
[23 5 9 4 25] [11 22 1 21 8]
[13 19 22 6 1] [ 6 20 3 25 16]
[16 14 8 24 2] [15 5 23 10 9]
[10 20 11 7 15] [24 2 14 7 17]
.
[ 3 24 4 20 18] [23 22 3 1 12]
[22 10 12 5 13] [21 9 17 13 7]
[17 1 21 25 6] [ 4 5 16 24 19]
[ 8 7 19 14 15] [ 2 10 25 11 18]
[ 9 23 11 2 16] [20 14 8 15 6]
CROSSREFS
Sequence in context: A253798 A022246 A227700 * A283209 A113939 A023686
KEYWORD
nonn,bref,hard,nice
AUTHOR
EXTENSIONS
a(n) not known for n >= 5.
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 23 17:43 EST 2024. Contains 370283 sequences. (Running on oeis4.)