login
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

%I #25 Feb 11 2024 02:36:21

%S 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,

%T 36,36,38,40,40,42,44,44,46,48,48,50,52,52,54,56,56,58,60,60,62,64,64,

%U 66,68,68,70,72,72,74,76,76,78,80,80,82,84,84,86

%N 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.

%C 2*[2n/3] is an upper bound for a(n). - _Jud McCranie_, Aug 12 2001

%C This bound is achieved for n=2, 4 and 6-65.

%C Conjecture: a(n) = 2*[2n/3] for n >= 6. - _Alexander D. Healy_, Feb 10 2024

%D Martin Gardner, The Last Recreations, Copernicus, NY, 1997, 274-283.

%H Alexander D. Healy, <a href="/A051754/a051754_1.pdf">Examples of optimal placements for n <= 65</a>

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

%K nonn,nice,more

%O 2,1

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

%E a(12)-a(65) from _Alexander D. Healy_, Feb 10 2024