cp's OEIS Frontend

A187298 Number of 3-step one space leftwards or up, two space rightwards or down asymmetric rook's tours on an n X n board summed over all starting positions.

%I A187298 #11 Apr 23 2018 08:37:43
%S A187298 0,2,36,98,198,330,494,690,918,1178,1470,1794,2150,2538,2958,3410,
%T A187298 3894,4410,4958,5538,6150,6794,7470,8178,8918,9690,10494,11330,12198,
%U A187298 13098,14030,14994,15990,17018,18078,19170,20294,21450,22638,23858,25110,26394
%N A187298 Number of 3-step one space leftwards or up, two space rightwards or down asymmetric rook's tours on an n X n board summed over all starting positions.
%C A187298 Row 3 of A187296.
%H A187298 R. H. Hardin, <a href="/A187298/b187298.txt">Table of n, a(n) for n = 1..50</a>
%F A187298 Empirical: a(n) = 16*n^2 - 44*n + 18 for n>3.
%F A187298 Conjectures from _Colin Barker_, Apr 23 2018: (Start)
%F A187298 G.f.: 2*x^2*(1 + 15*x - 2*x^2 + 5*x^3 - 3*x^4) / (1 - x)^3.
%F A187298 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
%F A187298 (End)
%e A187298 Some solutions for 4 X 4:
%e A187298 ..0..1..0..0....0..0..0..0....0..0..0..0....0..0..1..0....0..0..0..3
%e A187298 ..0..0..0..0....1..0..0..0....0..1..0..0....0..0..3..0....0..1..0..2
%e A187298 ..3..2..0..0....0..0..0..0....0..3..0..0....0..0..2..0....0..0..0..0
%e A187298 ..0..0..0..0....2..0..3..0....0..2..0..0....0..0..0..0....0..0..0..0
%Y A187298 Cf. A187296.
%K A187298 nonn
%O A187298 1,2
%A A187298 _R. H. Hardin_, Mar 08 2011