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A186865 Number of 6-step king's tours on an n X n board summed over all starting positions.

%I A186865 #22 Dec 18 2023 11:29:45
%S A186865 0,0,2240,22672,74072,156484,268048,408764,578632,777652,1005824,
%T A186865 1263148,1549624,1865252,2210032,2583964,2987048,3419284,3880672,
%U A186865 4371212,4890904,5439748,6017744,6624892,7261192,7926644,8621248,9345004,10097912,10879972,11691184
%N A186865 Number of 6-step king's tours on an n X n board summed over all starting positions.
%C A186865 From _J. Volkmar Schmidt_, Oct 18 2023: (Start)
%C A186865 Proof of a(n) = 14576*n^2 - 77924*n + 99292 for n>4 follows proof scheme from _David A. Corneth_ for A186864.
%C A186865 Distribution matrix of surrounding rectangles for 6-step walks is:
%C A186865   [0   0    0    0    0   2]
%C A186865   [0   0   96  576  448 124]
%C A186865   [0  96 1856 2272 1064 224]
%C A186865   [0 576 2272 1552  560 104]
%C A186865   [0 448 1064  560  168  28]
%C A186865   [2 124  224  104   28   4]
%C A186865 (End)
%H A186865 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F A186865 Empirical: a(n) = 14576*n^2 - 77924*n + 99292 for n>4.
%e A186865 Some solutions for 3X3
%e A186865 ..0..2..0....0..4..0....0..4..3....0..0..0....0..2..1....3..2..0....0..4..5
%e A186865 ..1..3..4....2..3..5....6..5..2....1..2..6....0..4..3....4..0..1....3..0..6
%e A186865 ..6..5..0....1..6..0....0..0..1....3..4..5....0..5..6....6..5..0....1..2..0
%Y A186865 Row 6 of A186861.
%K A186865 nonn
%O A186865 1,3
%A A186865 _R. H. Hardin_, Feb 27 2011