login
A051756
Consider the problem of placing N queens on an n X n board so that each queen attacks precisely 3 others. Sequence gives maximal number of queens.
3
4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 28, 30, 32, 34, 36, 40, 42, 44, 46, 48, 52, 54, 56, 58, 60, 64, 66, 68, 70, 72, 76, 78, 80, 82, 84, 88, 90, 92, 94, 96, 100, 102, 104, 106, 108, 112, 114, 116, 118, 120, 124, 126, 128, 130, 132, 136, 138, 140, 142, 144
OFFSET
2,1
COMMENTS
a(n) <= 2[(6n-2)/5]. - Jud McCranie, Aug 12 2001
Conjecture: a(n) = 2[(6n-2)/5] for n >= 2; verified up to n = 100. - Alexander D. Healy, Feb 11 2024
REFERENCES
Martin Gardner, The Last Recreations, Copernicus, NY, 1997, 274-283.
Peter Hayes, A Problem of Chess Queens, Journal of Recreational Mathematics, Baywood, 24(4), 1992, 264-271.
EXAMPLE
Examples from R. J. Mathar, May 01 2006: (Start)
==== n = 3
6 queens:
Q Q Q
Q - -
Q - Q
6 queens:
Q Q Q
- - -
Q Q Q
==== n = 4
8 queens:
Q Q Q Q
Q - - -
Q - - -
Q - - Q
8 queens:
Q Q Q Q
Q - - -
- - Q -
Q - - Q
8 queens:
Q Q Q Q
- - - -
- - - -
Q Q Q Q
8 queens:
Q Q - Q
- Q - -
- - Q -
Q - Q Q
==== n = 7
16 queens:
Q Q Q - Q - Q
- - - - - - Q
- - - Q - - -
Q - - - - - Q
- - - Q - - -
Q - - - - - -
Q - Q - Q Q Q
16 queens:
Q Q Q - - Q Q
- - - Q - - -
- - - - - - Q
Q - - - - - Q
Q - - - - - -
- - - Q - - -
Q Q - - Q Q Q
(End)
KEYWORD
nonn,nice
AUTHOR
Robert Trent (trentrd(AT)hotmail.com), Aug 23 2000
EXTENSIONS
More terms from Jud McCranie, Aug 12 2001
a(10)-a(61) from Alexander D. Healy, Feb 11 2024
STATUS
approved