cp's OEIS Frontend

A187512 Number of 7-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

%I A187512 #10 Apr 24 2018 09:19:57
%S A187512 0,0,20,330,1224,2726,4807,7458,10679,14470,18831,23762,29263,35334,
%T A187512 41975,49186,56967,65318,74239,83730,93791,104422,115623,127394,
%U A187512 139735,152646,166127,180178,194799,209990,225751,242082,258983,276454,294495
%N A187512 Number of 7-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.
%C A187512 Row 7 of A187507.
%H A187512 R. H. Hardin, <a href="/A187512/b187512.txt">Table of n, a(n) for n = 1..50</a>
%F A187512 Empirical: a(n) = 285*n^2 - 1624*n + 2210 for n>5.
%F A187512 Conjectures from _Colin Barker_, Apr 24 2018: (Start)
%F A187512 G.f.: x^3*(1 + x)*(20 + 250*x + 44*x^2 - 20*x^3 - 9*x^4) / (1 - x)^3.
%F A187512 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
%F A187512 (End)
%e A187512 Some solutions for 4 X 4:
%e A187512 ..0..0..0..0....1..2..0..0....0..5..3..1....0..0..1..2....4..5..6..0
%e A187512 ..0..7..0..0....0..3..4..0....0..6..4..2....0..7..5..3....2..3..7..0
%e A187512 ..1..5..6..0....0..7..5..0....0..7..0..0....0..0..6..4....0..1..0..0
%e A187512 ..2..3..4..0....0..0..6..0....0..0..0..0....0..0..0..0....0..0..0..0
%Y A187512 Cf. A187507.
%K A187512 nonn
%O A187512 1,3
%A A187512 _R. H. Hardin_, Mar 10 2011