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.

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

Author

Robert Trent (trentrd(AT)hotmail.com), Aug 23 2000

Keywords

• nonn
• nice
• more

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.

Links

• Alexander D. Healy, Examples of optimal placements for n <= 65

Crossrefs

Cf. A051755-A051759, A051567-A051571, A019654, A063724.

Extensions

a(12)-a(65) from Alexander D. Healy, Feb 10 2024