cp's OEIS Frontend

A187301 Number of 6-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 A187301 #10 Apr 23 2018 08:37:51
%S A187301 0,0,144,884,3006,6520,11896,18832,27478,37696,49508,62896,77860,
%T A187301 94400,112516,132208,153476,176320,200740,226736,254308,283456,314180,
%U A187301 346480,380356,415808,452836,491440,531620,573376,616708,661616,708100,756160
%N A187301 Number of 6-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 A187301 Row 6 of A187296.
%H A187301 R. H. Hardin, <a href="/A187301/b187301.txt">Table of n, a(n) for n = 1..50</a>
%F A187301 Empirical: a(n) = 788*n^2 - 4736*n + 6256 for n>9.
%F A187301 Conjectures from _Colin Barker_, Apr 23 2018: (Start)
%F A187301 G.f.: 2*x^3*(72 + 226*x + 393*x^2 + 5*x^3 + 235*x^4 - 151*x^5 + 75*x^6 - 69*x^7 + 11*x^8 - 9*x^9) / (1 - x)^3.
%F A187301 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.
%F A187301 (End)
%e A187301 Some solutions for 4 X 4:
%e A187301 ..0..2..1..3....0..2..1..3....0..5..0..6....0..1..0..0....6..5..0..0
%e A187301 ..0..0..0..5....0..0..6..5....2..4..3..0....0..0..5..0....0..4..0..0
%e A187301 ..0..0..0..4....0..0..0..4....1..0..0..0....0..2..4..3....1..3..2..0
%e A187301 ..0..0..0..6....0..0..0..0....0..0..0..0....0..0..6..0....0..0..0..0
%Y A187301 Cf. A187296.
%K A187301 nonn
%O A187301 1,3
%A A187301 _R. H. Hardin_, Mar 08 2011