%I #10 Apr 26 2018 08:45:41

%S 0,2,81,254,578,1030,1610,2318,3154,4118,5210,6430,7778,9254,10858,

%T 12590,14450,16438,18554,20798,23170,25670,28298,31054,33938,36950,

%U 40090,43358,46754,50278,53930,57710,61618,65654,69818,74110,78530,83078,87754,92558

%N Number of 3-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

%C Row 3 of A187857.

%H R. H. Hardin, <a href="/A187858/b187858.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 64*n^2 - 252*n + 238 for n>3.

%F Conjectures from _Colin Barker_, Apr 26 2018: (Start)

%F G.f.: x^2*(2 + 75*x + 17*x^2 + 57*x^3 - 23*x^4) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.

%F (End)

%e Some solutions for 4 X 4:

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

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

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

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

%Y Cf. A187857.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 14 2011