A186966 - OEIS

%I #11 May 10 2021 00:45:41

%S 0,24,296,1304,3808,8832,17672,31888,53312,84040,126440,183144,257056,

%T 351344,469448,615072,792192,1005048,1258152,1556280

%N Number of 3-turn queen's tours on an n X n board summed over all starting positions.

%C Row 3 of A186965.

%F Empirical: a(n) = 4*a(n-1)-5*a(n-2)+5*a(n-4)-4*a(n-5)+a(n-6).

%F Empirical: a(n) = -6*n+1/4-30*n^3+73*n^2/3+67*n^4/6-(-1)^n/4 with g.f. -8*x^2*(3+25*x+30*x^2+9*x^3) / ( (1+x)*(x-1)^5 ), all terms multiples of 8.

%e Some solutions for 3 X 3

%e ..2..0..3....3..0..0....2..3..0....3..0..0....0..3..0....0..0..1....3..1..0

%e ..0..0..0....0..2..0....0..0..0....1..2..0....0..0..2....0..0..0....0..2..0

%e ..1..0..0....0..0..1....1..0..0....0..0..0....0..0..1....2..0..3....0..0..0

%Y Cf. A186965.

%K nonn

%O 1,2

%A _R. H. Hardin_ Mar 01 2011