cp's OEIS Frontend

A187288 Number of 3-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

%I A187288 #10 Apr 22 2018 17:48:17
%S A187288 0,8,108,328,672,1128,1696,2376,3168,4072,5088,6216,7456,8808,10272,
%T A187288 11848,13536,15336,17248,19272,21408,23656,26016,28488,31072,33768,
%U A187288 36576,39496,42528,45672,48928,52296,55776,59368,63072,66888,70816,74856,79008
%N A187288 Number of 3-step one or two space at a time rook's tours on an n X n board summed over all starting positions.
%C A187288 Row 3 of A187286.
%H A187288 R. H. Hardin, <a href="/A187288/b187288.txt">Table of n, a(n) for n = 1..50</a>
%F A187288 Empirical: a(n) = 56*n^2 - 160*n + 72 for n>3.
%F A187288 Conjectures from _Colin Barker_, Apr 22 2018: (Start)
%F A187288 G.f.: 4*x^2*(2 + 21*x + 7*x^2 + x^3 - 3*x^4) / (1 - x)^3.
%F A187288 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
%F A187288 (End)
%e A187288 Some solutions for 4 X 4:
%e A187288 ..0..0..0..0....0..0..0..0....0..0..0..0....3..0..0..0....0..0..3..2
%e A187288 ..2..0..0..0....0..0..0..0....0..0..0..0....2..0..1..0....0..0..0..1
%e A187288 ..1..0..0..0....0..0..1..0....1..0..0..0....0..0..0..0....0..0..0..0
%e A187288 ..3..0..0..0....3..0..2..0....2..0..3..0....0..0..0..0....0..0..0..0
%Y A187288 Cf. A187286.
%K A187288 nonn
%O A187288 1,2
%A A187288 _R. H. Hardin_, Mar 08 2011