cp's OEIS Frontend

A187851 Number of 3-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.

%I A187851 #12 Apr 26 2018 08:38:59
%S A187851 0,24,304,1056,2312,4048,6264,8960,12136,15792,19928,24544,29640,
%T A187851 35216,41272,47808,54824,62320,70296,78752,87688,97104,107000,117376,
%U A187851 128232,139568,151384,163680,176456,189712,203448,217664,232360,247536,263192
%N A187851 Number of 3-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.
%C A187851 Row 3 of A187850.
%H A187851 R. H. Hardin, <a href="/A187851/b187851.txt">Table of n, a(n) for n = 1..50</a>
%F A187851 Empirical: a(n) = 240*n^2 - 904*n + 832 for n>3.
%F A187851 Conjectures from _Colin Barker_, Apr 26 2018: (Start)
%F A187851 G.f.: 8*x^2*(3 + 29*x + 27*x^2 + 4*x^3 - 3*x^4) / (1 - x)^3.
%F A187851 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
%F A187851 (End)
%e A187851 Some solutions for 4 X 4:
%e A187851 ..0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A187851 ..0..2..0..0....0..0..2..0....3..0..0..0....0..0..0..0....0..0..0..1
%e A187851 ..0..0..0..0....0..3..1..0....0..2..0..0....0..0..2..0....0..2..3..0
%e A187851 ..3..0..0..0....0..0..0..0....0..1..0..0....3..1..0..0....0..0..0..0
%Y A187851 Cf. A187850.
%K A187851 nonn
%O A187851 1,2
%A A187851 _R. H. Hardin_, Mar 14 2011