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