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A187379 Number of 5-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

%I A187379 #18 Aug 22 2025 05:56:01
%S A187379 0,0,40,188,487,924,1499,2212,3063,4052,5179,6444,7847,9388,11067,
%T A187379 12884,14839,16932,19163,21532,24039,26684,29467,32388,35447,38644,
%U A187379 41979,45452,49063,52812,56699,60724,64887,69188,73627,78204,82919,87772,92763,97892
%N A187379 Number of 5-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.
%H A187379 R. H. Hardin, <a href="/A187379/b187379.txt">Table of n, a(n) for n = 1..50</a>
%F A187379 Empirical: a(n) = 69*n^2 - 322*n + 372 for n>3.
%F A187379 Empirical g.f.: x^3*(40+68*x+43*x^2-13*x^3)/(1-x)^3. - _Colin Barker_, Jan 22 2012
%e A187379 Some solutions for 4X4
%e A187379 ..0..0..0..0....0..0..0..5....0..4..0..0....0..0..1..0....0..0..0..5
%e A187379 ..0..0..5..0....0..0..4..0....3..5..0..0....0..0..2..4....0..2..4..0
%e A187379 ..0..4..2..0....1..3..0..0....0..2..0..0....0..0..3..5....0..3..1..0
%e A187379 ..0..1..3..0....2..0..0..0....0..0..1..0....0..0..0..0....0..0..0..0
%Y A187379 Row 5 of A187377.
%K A187379 nonn
%O A187379 1,3
%A A187379 _R. H. Hardin_, Mar 09 2011