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

2,1

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.

Links

Table of n, a(n) for n=2..65.

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

Crossrefs

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

Sequence in context: A059867 A359182 A046971 * A108747 A116931 A206558

Adjacent sequences: A051751 A051752 A051753 * A051755 A051756 A051757

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