cp's OEIS Frontend

A187174 Number of 4-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.

%I A187174 #16 Apr 18 2022 17:48:34
%S A187174 0,0,0,8,48,176,384,664,1016,1440,1936,2504,3144,3856,4640,5496,6424,
%T A187174 7424,8496,9640,10856,12144,13504,14936,16440,18016,19664,21384,23176,
%U A187174 25040,26976,28984,31064,33216,35440,37736,40104,42544,45056,47640,50296
%N A187174 Number of 4-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.
%H A187174 R. H. Hardin, <a href="/A187174/b187174.txt">Table of n, a(n) for n = 1..50</a>
%F A187174 Empirical: a(n) = 36*n^2 - 260*n + 440 for n>5.
%F A187174 G.f.: 8*x^4*(1 + 3*x + 7*x^2 - x^3 - x^4) / (1 - x)^3 (conjectured). - _Colin Barker_, Apr 22 2018
%e A187174 Some solutions for 4 X 4:
%e A187174 ..0..0..1..0....0..0..3..0....0..0..4..0....0..0..2..0....0..0..1..0
%e A187174 ..4..0..0..0....4..0..0..0....3..0..0..0....1..0..0..0....2..0..0..0
%e A187174 ..0..0..0..2....0..0..0..2....0..0..0..1....0..0..0..3....0..0..0..4
%e A187174 ..0..3..0..0....0..1..0..0....0..2..0..0....0..4..0..0....0..3..0..0
%Y A187174 Row 4 of A187172.
%K A187174 nonn
%O A187174 1,4
%A A187174 _R. H. Hardin_, Mar 06 2011