cp's OEIS Frontend

A187381 Number of 7-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

%I A187381 #10 Apr 24 2018 06:43:32
%S A187381 0,0,18,324,1418,3448,6581,10688,15769,21824,28853,36856,45833,55784,
%T A187381 66709,78608,91481,105328,120149,135944,152713,170456,189173,208864,
%U A187381 229529,251168,273781,297368,321929,347464,373973,401456,429913,459344
%N A187381 Number of 7-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.
%C A187381 Row 7 of A187377.
%H A187381 R. H. Hardin, <a href="/A187381/b187381.txt">Table of n, a(n) for n = 1..50</a>
%F A187381 Empirical: a(n) = 487*n^2 - 3198*n + 5104 for n>5.
%F A187381 Conjectures from _Colin Barker_, Apr 24 2018: (Start)
%F A187381 G.f.: x^3*(18 + 270*x + 500*x^2 + 148*x^3 + 167*x^4 - 129*x^5) / (1 - x)^3.
%F A187381 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
%F A187381 (End)
%e A187381 Some solutions for 4 X 4:
%e A187381 ..0..0..0..6....0..0..0..0....0..0..7..0....0..5..3..1....0..0..2..0
%e A187381 ..0..3..5..7....0..1..0..0....4..6..0..0....0..6..4..2....0..0..3..1
%e A187381 ..0..4..2..0....0..2..4..6....5..3..1..0....0..7..0..0....0..0..4..6
%e A187381 ..0..1..0..0....0..3..5..7....0..0..2..0....0..0..0..0....0..0..5..7
%Y A187381 Cf. A187377.
%K A187381 nonn
%O A187381 1,3
%A A187381 _R. H. Hardin_, Mar 09 2011