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A051754
Consider problem of placing N queens on an n X n board so that each queen attacks precisely 1 other. Sequence gives maximal number of queens.
13
2, 2, 4, 4, 8, 8, 10, 12, 12, 14, 16, 16, 18, 20, 20, 22, 24, 24, 26, 28, 28, 30, 32, 32, 34, 36, 36, 38, 40, 40, 42, 44, 44, 46, 48, 48, 50, 52, 52, 54, 56, 56, 58, 60, 60, 62, 64, 64, 66, 68, 68, 70, 72, 72, 74, 76, 76, 78, 80, 80, 82, 84, 84, 86
OFFSET
2,1
COMMENTS
2*[2n/3] is an upper bound for a(n). - Jud McCranie, Aug 12 2001
This bound is achieved for n=2, 4 and 6-65.
Conjecture: a(n) = 2*[2n/3] for n >= 6. - Alexander D. Healy, Feb 10 2024
REFERENCES
Martin Gardner, The Last Recreations, Copernicus, NY, 1997, 274-283.
KEYWORD
nonn,nice,more
AUTHOR
Robert Trent (trentrd(AT)hotmail.com), Aug 23 2000
EXTENSIONS
a(12)-a(65) from Alexander D. Healy, Feb 10 2024
STATUS
approved