cp's OEIS Frontend

A187854 Number of 6-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.

%I A187854 #10 Apr 26 2018 08:38:50
%S A187854 0,0,16032,292776,1400168,3807828,7700944,13082348,19910456,28160124,
%T A187854 37824352,48902340,61394088,75299596,90618864,107351892,125498680,
%U A187854 145059228,166033536,188421604,212223432,237439020,264068368,292111476
%N A187854 Number of 6-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.
%C A187854 Row 6 of A187850.
%H A187854 R. H. Hardin, <a href="/A187854/b187854.txt">Table of n, a(n) for n = 1..50</a>
%F A187854 Empirical: a(n) = 706880*n^2 - 5180252*n + 9274644 for n>9.
%F A187854 Conjectures from _Colin Barker_, Apr 26 2018: (Start)
%F A187854 G.f.: 4*x^3*(4008 + 61170*x + 142484*x^2 + 117405*x^3 + 46297*x^4 + 708*x^5 - 10396*x^6 - 6286*x^7 - 1750*x^8 - 200*x^9) / (1 - x)^3.
%F A187854 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.
%F A187854 (End)
%e A187854 Some solutions for 4 X 4:
%e A187854 ..0..5..4..0....0..0..0..0....0..0..0..0....0..4..0..6....0..0..2..0
%e A187854 ..1..6..3..0....0..4..0..0....0..1..4..6....0..0..5..0....0..0..3..1
%e A187854 ..0..0..2..0....5..3..0..0....0..0..5..2....0..1..3..0....0..0..5..0
%e A187854 ..0..0..0..0....1..2..6..0....0..3..0..0....0..0..0..2....6..4..0..0
%Y A187854 Cf. A187850.
%K A187854 nonn
%O A187854 1,3
%A A187854 _R. H. Hardin_, Mar 14 2011