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%I #11 Apr 25 2018 11:39:10
%S 0,0,9,36,100,196,324,484,676,900,1156,1444,1764,2116,2500,2916,3364,
%T 3844,4356,4900,5476,6084,6724,7396,8100,8836,9604,10404,11236,12100,
%U 12996,13924,14884,15876,16900,17956,19044,20164,21316,22500,23716,24964
%N Number of 3-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-bishop's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.
%C Row 3 of A187606.
%H R. H. Hardin, <a href="/A187607/b187607.txt">Table of n, a(n) for n = 1..50</a>
%F Empirical: a(n) = 16*n^2 - 80*n + 100 for n>3.
%F Conjectures from _Colin Barker_, Apr 25 2018: (Start)
%F G.f.: x^3*(9 + 9*x + 19*x^2 - 5*x^3) / (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 5 X 5:
%e ..0..0..0..0..0....0..0..0..0..0....0..0..0..1..0....0..0..0..3..0
%e ..0..0..3..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..2
%e ..0..0..0..2..0....0..0..1..0..0....0..0..2..0..0....0..0..1..0..0
%e ..0..0..0..0..1....3..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e ..0..0..0..0..0....0..2..0..0..0....0..0..0..0..3....0..0..0..0..0
%Y Cf. A187606.
%K nonn
%O 1,3
%A _R. H. Hardin_, Mar 11 2011
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