cp's OEIS Frontend

A187173 Number of 3-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.

%I A187173 #15 Apr 22 2018 17:46:36
%S A187173 0,0,0,16,60,128,220,336,476,640,828,1040,1276,1536,1820,2128,2460,
%T A187173 2816,3196,3600,4028,4480,4956,5456,5980,6528,7100,7696,8316,8960,
%U A187173 9628,10320,11036,11776,12540,13328,14140,14976,15836,16720,17628,18560,19516,20496
%N A187173 Number of 3-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.
%C A187173 Row 3 of A187172.
%H A187173 R. H. Hardin, <a href="/A187173/b187173.txt">Table of n, a(n) for n = 1..50</a>
%F A187173 Empirical: a(n) = 12*n^2 - 64*n + 80 for n>3.
%F A187173 G.f.: 4*x^4*(4 - x)*(1 + x) / (1 - x)^3 (conjectured). - _Colin Barker_, Apr 22 2018
%e A187173 Some solutions for 4 X 4:
%e A187173 ..0..0..2..0....0..0..1..0....0..0..0..0....0..0..0..0....0..0..1..0
%e A187173 ..3..0..0..0....0..0..0..0....3..0..0..0....0..0..2..0....2..0..0..0
%e A187173 ..0..0..0..1....0..0..0..2....0..0..0..1....3..0..0..0....0..0..0..0
%e A187173 ..0..0..0..0....0..3..0..0....0..2..0..0....0..0..0..1....0..3..0..0
%Y A187173 Cf. A187172.
%K A187173 nonn
%O A187173 1,4
%A A187173 _R. H. Hardin_, Mar 06 2011