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%I #10 Apr 24 2018 08:07:34
%S 0,0,0,340,3060,10320,24892,46412,75567,111492,154187,203652,259887,
%T 322892,392667,469212,552527,642612,739467,843092,953487,1070652,
%U 1194587,1325292,1462767,1607012,1758027,1915812,2080367,2251692,2429787,2614652
%N Number of 9-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.
%C Row 9 of A187377.
%H R. H. Hardin, <a href="/A187383/b187383.txt">Table of n, a(n) for n = 1..50</a>
%F Empirical: a(n) = 3385*n^2 - 28390*n + 56892 for n>7.
%F Conjectures from _Colin Barker_, Apr 24 2018: (Start)
%F G.f.: x^4*(340 + 2040*x + 2160*x^2 + 2772*x^3 - 364*x^4 + 687*x^5 - 865*x^6) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
%F (End)
%Y Cf. A187377.
%K nonn
%O 1,4
%A _R. H. Hardin_, Mar 09 2011
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