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A187861 Number of 6-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. 1

%I

%S 0,0,846,9932,47962,126397,262409,452766,707541,1017934,1387600,

%T 1813854,2296696,2836126,3432144,4084750,4793944,5559726,6382096,

%U 7261054,8196600,9188734,10237456,11342766,12504664,13723150,14998224,16329886,17718136

%N Number of 6-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 6 of A187857.

%H R. H. Hardin, <a href="/A187861/b187861.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 28294*n^2 - 224508*n + 433614 for n>9.

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

%F G.f.: x^3*(846 + 7394*x + 20704*x^2 + 11461*x^3 + 17172*x^4 - 3232*x^5 + 10073*x^6 - 8800*x^7 + 3655*x^8 - 2685*x^9) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.

%F (End)

%e Some solutions for 4 X 4:

%e ..0..0..0..0....5..0..6..0....0..3..2..6....0..0..1..0....0..0..0..1

%e ..3..2..4..0....4..3..0..0....1..0..0..5....0..5..0..0....0..0..3..0

%e ..0..1..0..0....0..0..2..0....0..0..0..4....3..2..4..0....6..5..2..0

%e ..6..5..0..0....1..0..0..0....0..0..0..0....6..0..0..0....0..0..4..0

%Y Cf. A187857.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 14 2011

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Last modified January 27 10:32 EST 2022. Contains 350607 sequences. (Running on oeis4.)