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A186862 Number of 3-step king's tours on an n X n board summed over all starting positions.

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