cp's OEIS Frontend

A187191 Number of 4-turn rook's tours on an n X n board summed over all starting positions.

%I A187191 #18 Aug 22 2025 05:56:49
%S A187191 0,8,288,2208,9200,27720,68208,146048,282528,505800,851840,1365408,
%T A187191 2101008,3123848,4510800,6351360,8748608,11820168,15699168,20535200,
%U A187191 26495280,33764808,42548528,53071488,65580000,80342600,97651008
%N A187191 Number of 4-turn rook's tours on an n X n board summed over all starting positions.
%H A187191 R. H. Hardin, <a href="/A187191/b187191.txt">Table of n, a(n) for n = 1..28</a>
%F A187191 Empirical: a(n) = 8*n^5 - 34*n^4 + 48*n^3 - 22*n^2.
%F A187191 Empirical g.f.: 8*x^2*(1+30*x+75*x^2+14*x^3)/(1-x)^6. - _Colin Barker_, Jan 22 2012
%e A187191 Some solutions for 3X3
%e A187191 ..0..4..0....2..1..0....0..1..2....1..0..0....0..0..4....4..2..3....3..2..0
%e A187191 ..2..3..1....3..0..0....4..0..3....2..3..4....0..1..2....0..0..0....0..0..0
%e A187191 ..0..0..0....4..0..0....0..0..0....0..0..0....0..0..3....0..1..0....4..1..0
%Y A187191 Row 4 of A187189.
%K A187191 nonn
%O A187191 1,2
%A A187191 _R. H. Hardin_, Mar 06 2011