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A187860 Number of 5-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.

%I A187860 #10 Apr 26 2018 08:59:52
%S A187860 0,0,486,3320,11986,26836,50378,81124,120051,166504,220483,281988,
%T A187860 351019,427576,511659,603268,702403,809064,923251,1044964,1174203,
%U A187860 1310968,1455259,1607076,1766419,1933288,2107683,2289604,2479051,2676024,2880523
%N A187860 Number of 5-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 A187860 Row 5 of A187857.
%H A187860 R. H. Hardin, <a href="/A187860/b187860.txt">Table of n, a(n) for n = 1..50</a>
%F A187860 Empirical: a(n) = 3763*n^2 - 25044*n + 40644 for n>7.
%F A187860 Conjectures from _Colin Barker_, Apr 26 2018: (Start)
%F A187860 G.f.: x^3*(486 + 1862*x + 3484*x^2 + 352*x^3 + 2508*x^4 - 1488*x^5 + 977*x^6 - 655*x^7) / (1 - x)^3.
%F A187860 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
%F A187860 (End)
%e A187860 Some solutions for 4 X 4:
%e A187860 ..0..1..0..0....0..0..2..0....0..0..0..0....0..0..5..0....0..0..0..0
%e A187860 ..0..0..0..4....0..0..1..0....1..0..0..0....4..1..0..0....0..4..3..5
%e A187860 ..0..2..0..3....5..4..3..0....5..0..0..0....0..3..0..0....0..0..2..0
%e A187860 ..0..0..5..0....0..0..0..0....4..3..2..0....0..2..0..0....0..0..0..1
%Y A187860 Cf. A187857.
%K A187860 nonn
%O A187860 1,3
%A A187860 _R. H. Hardin_, Mar 14 2011