cp's OEIS Frontend

A187292 Number of 7-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

%I A187292 #11 Apr 23 2018 08:37:52
%S A187292 0,0,2304,47648,228512,616752,1241936,2102944,3192912,4505424,6037932,
%T A187292 7789392,9759616,11948560,14356224,16982608,19827712,22891536,
%U A187292 26174080,29675344,33395328,37334032,41491456,45867600,50462464,55276048,60308352
%N A187292 Number of 7-step one or two space at a time rook's tours on an n X n board summed over all starting positions.
%C A187292 Row 7 of A187286.
%H A187292 R. H. Hardin, <a href="/A187292/b187292.txt">Table of n, a(n) for n = 1..50</a>
%F A187292 Empirical: a(n) = 109360*n^2 - 763776*n + 1206864 for n>11.
%F A187292 Conjectures from _Colin Barker_, Apr 23 2018: (Start)
%F A187292 G.f.: 4*x^3*(576 + 10184*x + 23120*x^2 + 17964*x^3 + 7392*x^4 - 280*x^5 - 1716*x^6 - 1604*x^7 - 637*x^8 - 261*x^9 - 47*x^10 - 11*x^11) / (1 - x)^3.
%F A187292 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>14.
%F A187292 (End)
%e A187292 Some solutions for 4 X 4:
%e A187292 ..0..0..0..0....0..0..0..0....0..1..0..0....2..3..0..0....6..5..7..0
%e A187292 ..0..5..6..4....0..0..7..0....3..2..7..0....1..5..7..6....0..0..0..0
%e A187292 ..1..2..0..3....4..1..5..0....5..0..6..0....0..4..0..0....0..4..0..3
%e A187292 ..0..0..7..0....3..2..6..0....4..0..0..0....0..0..0..0....0..1..0..2
%Y A187292 Cf. A187286.
%K A187292 nonn
%O A187292 1,3
%A A187292 _R. H. Hardin_, Mar 08 2011