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A187587 Number of 4-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

%I A187587 #17 Aug 23 2025 00:02:36
%S A187587 0,5,84,286,604,1038,1588,2254,3036,3934,4948,6078,7324,8686,10164,
%T A187587 11758,13468,15294,17236,19294,21468,23758,26164,28686,31324,34078,
%U A187587 36948,39934,43036,46254,49588,53038,56604,60286,64084,67998,72028,76174,80436,84814
%N A187587 Number of 4-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.
%H A187587 R. H. Hardin, <a href="/A187587/b187587.txt">Table of n, a(n) for n = 1..50</a>
%F A187587 Empirical: a(n) = 58*n^2 - 204*n + 174 for n>2.
%F A187587 Empirical g.f.: x^2*(5+69*x+49*x^2-7*x^3)/(1-x)^3. - _Colin Barker_, Jan 22 2012
%e A187587 Some solutions for 4X4
%e A187587 ..0..0..0..0....0..0..0..0....0..2..0..0....0..0..0..0....0..0..2..4
%e A187587 ..0..0..1..0....0..0..0..0....1..3..0..0....0..0..0..0....0..1..3..0
%e A187587 ..0..0..2..3....0..0..2..3....0..4..0..0....0..0..2..4....0..0..0..0
%e A187587 ..0..0..0..4....0..1..0..4....0..0..0..0....0..1..3..0....0..0..0..0
%Y A187587 Row 4 of A187586.
%K A187587 nonn,changed
%O A187587 1,2
%A A187587 _R. H. Hardin_, Mar 11 2011