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A187588 Number of 5-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

%I A187588 #12 May 15 2023 14:39:30
%S A187588 0,0,106,578,1484,2794,4508,6626,9148,12074,15404,19138,23276,27818,
%T A187588 32764,38114,43868,50026,56588,63554,70924,78698,86876,95458,104444,
%U A187588 113834,123628,133826,144428,155434,166844,178658,190876,203498,216524
%N A187588 Number of 5-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.
%C A187588 Row 5 of A187586.
%H A187588 R. H. Hardin, <a href="/A187588/b187588.txt">Table of n, a(n) for n = 1..50</a>
%F A187588 Empirical: a(n) = 202*n^2 - 912*n + 994 for n>3.
%F A187588 Empirical G.f.: 2*x^3*(53+130*x+34*x^2-15*x^3)/(1-x)^3. [_Colin Barker_, Jan 22 2012]
%e A187588 Some solutions for 4 X 4
%e A187588 ..0..5..0..0....0..5..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A187588 ..0..0..4..0....0..3..4..0....0..0..4..5....0..0..0..0....0..0..2..0
%e A187588 ..0..0..1..3....0..1..2..0....0..0..2..3....0..0..2..4....0..1..3..5
%e A187588 ..0..0..2..0....0..0..0..0....0..0..0..1....0..1..3..5....0..0..4..0
%Y A187588 Cf. A187586.
%K A187588 nonn
%O A187588 1,3
%A A187588 _R. H. Hardin_, Mar 11 2011