A187384 - OEIS

%I #10 Apr 24 2018 08:47:02

%S 0,0,0,280,3792,17052,44464,92628,159328,245946,350386,472648,612732,

%T 770638,946366,1139916,1351288,1580482,1827498,2092336,2374996,

%U 2675478,2993782,3329908,3683856,4055626,4445218,4852632,5277868,5720926,6181806

%N Number of 10-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

%C Row 10 of A187377.

%H R. H. Hardin, <a href="/A187384/b187384.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 8911*n^2 - 82691*n + 181756 for n>8.

%F Conjectures from _Colin Barker_, Apr 24 2018: (Start)

%F G.f.: 2*x^4*(140 + 1476*x + 3258*x^2 + 2202*x^3 + 3300*x^4 - 1108*x^5 + 691*x^6 - 1048*x^7) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.

%F (End)

%Y Cf. A187377.

%K nonn

%O 1,4

%A _R. H. Hardin_, Mar 09 2011