A186966 Number of 3-turn queen's tours on an n X n board summed over all starting positions.
0, 24, 296, 1304, 3808, 8832, 17672, 31888, 53312, 84040, 126440, 183144, 257056, 351344, 469448, 615072, 792192, 1005048, 1258152, 1556280
Offset: 1
Keywords
Examples
Some solutions for 3 X 3 ..2..0..3....3..0..0....2..3..0....3..0..0....0..3..0....0..0..1....3..1..0 ..0..0..0....0..2..0....0..0..0....1..2..0....0..0..2....0..0..0....0..2..0 ..1..0..0....0..0..1....1..0..0....0..0..0....0..0..1....2..0..3....0..0..0
Crossrefs
Cf. A186965.
Formula
Empirical: a(n) = 4*a(n-1)-5*a(n-2)+5*a(n-4)-4*a(n-5)+a(n-6).
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.
Comments