cp's OEIS Frontend

A187178 Number of 8-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.

%I A187178 #10 Apr 22 2018 17:47:47
%S A187178 0,0,0,0,0,0,280,1784,5944,14072,27104,45288,68400,96048,128064,
%T A187178 164424,205128,250176,299568,353304,411384,473808,540576,611688,
%U A187178 687144,766944,851088,939576,1032408,1129584,1231104,1336968,1447176,1561728,1680624
%N A187178 Number of 8-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.
%C A187178 Row 8 of A187172.
%H A187178 R. H. Hardin, <a href="/A187178/b187178.txt">Table of n, a(n) for n = 1..50</a>
%F A187178 Empirical: a(n) = 2172*n^2 - 30972*n + 103944 for n>13.
%F A187178 Empirical g.f.: 8*x^7*(35 + 118*x + 179*x^2 + 164*x^3 + 117*x^4 + 31*x^5 - 28*x^6 - 49*x^7 - 21*x^8 - 3*x^9) / (1 - x)^3. - _Colin Barker_, Apr 22 2018
%e A187178 Some solutions for 7 X 7:
%e A187178 ..0..0..0..4..0..0..0....0..0..0..0..4..0..0....0..0..0..0..0..0..0
%e A187178 ..0..5..0..0..0..0..0....0..0..3..0..0..0..0....0..0..0..0..8..0..0
%e A187178 ..0..0..0..0..3..0..0....2..0..0..0..0..5..0....0..0..7..0..0..0..0
%e A187178 ..0..0..6..0..0..0..0....0..0..0..8..0..0..0....6..0..0..0..0..1..0
%e A187178 ..7..0..0..0..0..2..0....0..1..0..0..0..0..6....0..0..0..4..0..0..0
%e A187178 ..0..0..0..1..0..0..0....0..0..0..0..7..0..0....0..5..0..0..0..0..2
%e A187178 ..0..8..0..0..0..0..0....0..0..0..0..0..0..0....0..0..0..0..3..0..0
%Y A187178 Cf. A187172.
%K A187178 nonn
%O A187178 1,7
%A A187178 _R. H. Hardin_, Mar 06 2011