cp's OEIS Frontend

A187853 Number of 5-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.

%I A187853 #10 Apr 26 2018 08:38:32
%S A187853 0,0,5328,49776,177040,408048,744696,1183632,1723120,2362864,3102864,
%T A187853 3943120,4883632,5924400,7065424,8306704,9648240,11090032,12632080,
%U A187853 14274384,16016944,17859760,19802832,21846160,23989744,26233584,28577680
%N A187853 Number of 5-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.
%C A187853 Row 5 of A187850.
%H A187853 R. H. Hardin, <a href="/A187853/b187853.txt">Table of n, a(n) for n = 1..50</a>
%F A187853 Empirical: a(n) = 50128*n^2 - 312688*n + 476944 for n>7.
%F A187853 Conjectures from _Colin Barker_, Apr 26 2018: (Start)
%F A187853 G.f.: 8*x^3*(666 + 4224*x + 5462*x^2 + 2616*x^3 + 237*x^4 - 419*x^5 - 217*x^6 - 37*x^7) / (1 - x)^3.
%F A187853 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
%F A187853 (End)
%e A187853 Some solutions for 4 X 4:
%e A187853 ..0..5..0..0....4..1..0..0....2..0..0..0....0..0..0..0....0..5..0..0
%e A187853 ..0..0..1..2....0..3..2..0....1..0..0..0....0..0..2..0....0..0..0..3
%e A187853 ..0..0..4..3....0..5..0..0....0..3..0..0....0..3..5..1....0..0..4..2
%e A187853 ..0..0..0..0....0..0..0..0....4..5..0..0....4..0..0..0....0..1..0..0
%Y A187853 Cf. A187850.
%K A187853 nonn
%O A187853 1,3
%A A187853 _R. H. Hardin_, Mar 14 2011