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%I #13 Apr 19 2022 03:34:12
%S 0,8,108,480,1400,3240,6468,11648,19440,30600,45980,66528,93288,
%T 127400,170100,222720,286688,363528,454860,562400,687960,833448,
%U 1000868,1192320,1410000,1656200,1933308,2243808,2590280,2975400
%N Number of 3-turn rook's tours on an n X n board summed over all starting positions
%F Empirical: a(n) = 4*n^4 - 10*n^3 + 6*n^2.
%F Empirical G.f.: 4*x^2*(2+17*x+5*x^2)/(1-x)^5. - _Colin Barker_, Jan 22 2012
%e Some solutions for 3X3
%e ..0..0..3....0..2..3....1..0..2....0..0..3....0..3..0....0..0..0....3..2..0
%e ..0..1..2....0..1..0....0..0..0....0..0..2....0..2..1....0..2..3....0..0..0
%e ..0..0..0....0..0..0....0..0..3....0..0..1....0..0..0....0..1..0....0..1..0
%Y Row 3 of A187189.
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 06 2011