cp's OEIS Frontend

A187300 Number of 5-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 A187300 #10 Apr 23 2018 08:39:09
%S A187300 0,0,90,416,1208,2400,4092,6208,8766,11752,15166,19008,23278,27976,
%T A187300 33102,38656,44638,51048,57886,65152,72846,80968,89518,98496,107902,
%U A187300 117736,127998,138688,149806,161352,173326,185728,198558,211816,225502,239616
%N A187300 Number of 5-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 A187300 Row 5 of A187296.
%H A187300 R. H. Hardin, <a href="/A187300/b187300.txt">Table of n, a(n) for n = 1..50</a>
%F A187300 Empirical: a(n) = 214*n^2 - 1080*n + 1152 for n>7.
%F A187300 Conjectures from _Colin Barker_, Apr 23 2018: (Start)
%F A187300 G.f.: 2*x^3*(45 + 73*x + 115*x^2 - 33*x^3 + 50*x^4 - 38*x^5 + 9*x^6 - 7*x^7) / (1 - x)^3.
%F A187300 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
%F A187300 (End)
%e A187300 Some solutions for 4 X 4:
%e A187300 ..0..0..0..0....0..4..3..2....0..0..0..0....0..0..0..0....0..0..0..0
%e A187300 ..0..0..2..1....0..0..0..1....5..4..3..0....5..1..0..0....3..0..4..0
%e A187300 ..0..0..0..0....0..5..0..0....0..0..2..0....4..0..0..0....2..0..0..0
%e A187300 ..0..4..3..5....0..0..0..0....0..0..1..0....3..2..0..0....1..0..5..0
%Y A187300 Cf. A187296.
%K A187300 nonn
%O A187300 1,3
%A A187300 _R. H. Hardin_, Mar 08 2011