cp's OEIS Frontend

A187289 Number of 4-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

%I A187289 #10 Apr 22 2018 17:48:27
%S A187289 0,8,288,1256,3084,5712,9120,13288,18216,23904,30352,37560,45528,
%T A187289 54256,63744,73992,85000,96768,109296,122584,136632,151440,167008,
%U A187289 183336,200424,218272,236880,256248,276376,297264,318912,341320,364488,388416
%N A187289 Number of 4-step one or two space at a time rook's tours on an n X n board summed over all starting positions.
%C A187289 Row 4 of A187286.
%H A187289 R. H. Hardin, <a href="/A187289/b187289.txt">Table of n, a(n) for n = 1..50</a>
%F A187289 Empirical: a(n) = 380*n^2 - 1532*n + 1224 for n>5.
%F A187289 Conjectures from _Colin Barker_, Apr 22 2018: (Start)
%F A187289 G.f.: 4*x^2*(2 + 66*x + 104*x^2 + 43*x^3 - 15*x^4 - 5*x^5 - 5*x^6) / (1 - x)^3.
%F A187289 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
%F A187289 (End)
%e A187289 Some solutions for 4 X 4:
%e A187289 ..0..1..0..0....0..0..0..0....1..0..0..0....0..0..0..0....0..1..0..0
%e A187289 ..0..2..0..0....0..0..4..0....0..0..0..0....0..0..1..0....3..2..0..0
%e A187289 ..0..4..0..0....0..0..0..0....2..3..0..0....0..0..2..3....4..0..0..0
%e A187289 ..0..3..0..0....0..1..3..2....0..4..0..0....0..0..0..4....0..0..0..0
%Y A187289 Cf. A187286.
%K A187289 nonn
%O A187289 1,2
%A A187289 _R. H. Hardin_, Mar 08 2011