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A186866 Number of 7-step king's tours on an n X n board summed over all starting positions.

%I A186866 #21 Dec 18 2023 11:30:45
%S A186866 0,0,2984,68272,296360,722384,1335984,2129440,3102752,4255920,5588944,
%T A186866 7101824,8794560,10667152,12719600,14951904,17364064,19956080,
%U A186866 22727952,25679680,28811264,32122704,35614000,39285152,43136160,47167024
%N A186866 Number of 7-step king's tours on an n X n board summed over all starting positions.
%C A186866 From _J. Volkmar Schmidt_, Oct 24 2023 (Start)
%C A186866 Proof of a(n) follows proof scheme from _David A. Corneth_ for A186864.
%C A186866 Distribution matrix of surrounding rectangles for 7-step walks is:
%C A186866  [0    0    0     0    0    0   2]
%C A186866  [0    0    0   800 1600 1024 252]
%C A186866  [0    0 2984  9780 7904 3360 644]
%C A186866  [0  800 9780 12416 6636 2272 388]
%C A186866  [0 1600 7904  6636 2912  864 136]
%C A186866  [0 1024 3360  2272  864  224  32]
%C A186866  [2  252  644   388  136   32   4]
%C A186866 (End)
%H A186866 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F A186866 Empirical: a(n) = 89928*n^2 - 555464*n + 817760 for n>5.
%e A186866 Some solutions for 3X3
%e A186866 ..0..2..1....0..2..0....6..0..0....1..7..6....1..2..3....7..2..1....6..5..0
%e A186866 ..4..3..0....3..7..1....7..5..2....2..0..5....0..4..7....3..6..0....7..4..1
%e A186866 ..5..6..7....4..5..6....4..3..1....3..4..0....0..6..5....5..4..0....0..2..3
%Y A186866 Row 7 of A186861.
%K A186866 nonn
%O A186866 1,3
%A A186866 _R. H. Hardin_, Feb 27 2011