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%I #40 Dec 18 2023 11:23:56
%S 0,24,160,408,768,1240,1824,2520,3328,4248,5280,6424,7680,9048,10528,
%T 12120,13824,15640,17568,19608,21760,24024,26400,28888,31488,34200,
%U 37024,39960,43008,46168,49440,52824,56320,59928,63648,67480,71424,75480,79648,83928,88320,92824
%N Number of 3-step king's tours on an n X n board summed over all starting positions.
%H J. Volkmar Schmidt, <a href="/A186862/b186862.txt">Table of n, a(n) for n = 1..50</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F a(n) = 56*n^2 - 144*n + 88 = 8*(n-1)*(7*n-11).
%F G.f.: 8*x^2*(3+11*x)/(1-x)^3. - _Colin Barker_, Jan 22 2012
%e Some solutions for 3 X 3:
%e 0 0 0 0 1 0 2 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 3
%e 3 0 0 2 3 0 3 0 0 0 2 3 0 1 0 0 0 0 2 0 0 0 2 0
%e 2 1 0 0 0 0 0 0 0 0 0 0 3 2 0 1 2 3 3 0 0 0 0 0
%Y Row 3 of A186861.
%K nonn,easy
%O 1,2
%A _R. H. Hardin_, Feb 27 2011
%E a(29)-a(42) from _J. Volkmar Schmidt_, Sep 03 2023
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