cp's OEIS Frontend

A187176 Number of 6-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.

%I A187176 #13 Apr 22 2018 17:47:33
%S A187176 0,0,0,0,0,88,496,1440,3064,5344,8208,11640,15640,20208,25344,31048,
%T A187176 37320,44160,51568,59544,68088,77200,86880,97128,107944,119328,131280,
%U A187176 143800,156888,170544,184768,199560,214920,230848,247344,264408,282040
%N A187176 Number of 6-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.
%C A187176 Row 6 of A187172.
%H A187176 R. H. Hardin, <a href="/A187176/b187176.txt">Table of n, a(n) for n = 1..50</a>
%F A187176 Empirical: a(n) = 284*n^2 - 3100*n + 7944 for n>9.
%F A187176 G.f.: 8*x^6*(11 + 29*x + 27*x^2 + 18*x^3 - 3*x^4 - 9*x^5 - 2*x^6) / (1 - x)^3 (conjectured). - _Colin Barker_, Apr 22 2018
%e A187176 Some solutions for 6 X 6:
%e A187176 ..0..0..0..5..0..0....0..0..0..0..0..0....0..0..4..0..0..0....0..0..0..6..0..0
%e A187176 ..0..6..0..0..0..0....0..0..0..0..6..0....3..0..0..0..0..0....0..1..0..0..0..0
%e A187176 ..0..0..0..0..4..0....0..0..5..0..0..0....0..0..0..5..0..0....0..0..0..0..5..0
%e A187176 ..0..0..1..0..0..0....4..0..0..0..0..1....0..2..0..0..0..0....0..0..2..0..0..0
%e A187176 ..0..0..0..0..0..3....0..0..0..2..0..0....0..0..0..0..6..0....0..0..0..0..0..4
%e A187176 ..0..0..0..2..0..0....0..3..0..0..0..0....0..0..1..0..0..0....0..0..0..3..0..0
%Y A187176 Cf. A187172.
%K A187176 nonn
%O A187176 1,6
%A A187176 _R. H. Hardin_, Mar 06 2011