cp's OEIS Frontend

A187291 Number of 6-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

%I A187291 #12 Apr 22 2018 17:46:22
%S A187291 0,0,1440,15424,57288,134408,248208,397152,580328,797160,1047532,
%T A187291 1331408,1648788,1999672,2384060,2801952,3253348,3738248,4256652,
%U A187291 4808560,5393972,6012888,6665308,7351232,8070660,8823592,9610028,10429968,11283412
%N A187291 Number of 6-step one or two space at a time rook's tours on an n X n board summed over all starting positions.
%C A187291 Row 6 of A187286.
%H A187291 R. H. Hardin, <a href="/A187291/b187291.txt">Table of n, a(n) for n = 1..50</a>
%F A187291 Empirical: a(n) = 16752*n^2 - 101420*n + 136160 for n>9.
%F A187291 Conjectures from _Colin Barker_, Apr 22 2018: (Start)
%F A187291 G.f.: 4*x^3*(360 + 2776*x + 3834*x^2 + 1844*x^3 + 356*x^4 - 384*x^5 - 228*x^6 - 144*x^7 - 29*x^8 - 9*x^9) / (1 - x)^3.
%F A187291 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.
%F A187291 (End)
%e A187291 Some solutions for 4 X 4:
%e A187291   0 2 1 3    0 0 3 4    0 0 0 0    0 0 1 2    1 2 3 0
%e A187291   0 0 0 0    0 0 0 0    0 0 0 0    0 5 6 4    0 5 4 0
%e A187291   0 5 0 4    0 0 2 5    1 2 4 3    0 0 0 3    0 6 0 0
%e A187291   0 6 0 0    0 0 1 6    0 6 5 0    0 0 0 0    0 0 0 0
%Y A187291 Cf. A187286.
%K A187291 nonn
%O A187291 1,3
%A A187291 _R. H. Hardin_, Mar 08 2011