cp's OEIS Frontend

A187177 Number of 7-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.

%I A187177 #13 Apr 22 2018 17:47:40
%S A187177 0,0,0,0,0,16,368,1600,4284,8760,15104,23144,32764,43944,56684,70984,
%T A187177 86844,104264,123244,143784,165884,189544,214764,241544,269884,299784,
%U A187177 331244,364264,398844,434984,472684,511944,552764,595144,639084,684584
%N A187177 Number of 7-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.
%C A187177 Row 7 of A187172.
%H A187177 R. H. Hardin, <a href="/A187177/b187177.txt">Table of n, a(n) for n = 1..50</a>
%F A187177 Empirical: a(n) = 780*n^2 - 9880*n + 29384 for n>11.
%F A187177 G.f.: 4*x^6*(4 + 80*x + 136*x^2 + 143*x^3 + 85*x^4 + 19*x^5 - 43*x^6 - 29*x^7 - 5*x^8) / (1 - x)^3 (conjectured). - _Colin Barker_, Apr 22 2018
%e A187177 Some solutions for 6 X 6:
%e A187177 ..0..0..3..0..0..0....0..1..0..0..0..0....0..0..0..6..0..0....0..0..0..4..0..0
%e A187177 ..4..0..0..0..0..1....0..0..0..0..7..0....0..7..0..0..0..0....0..5..0..0..0..0
%e A187177 ..0..0..0..2..0..0....0..0..2..0..0..0....0..0..0..0..5..0....0..0..0..0..3..0
%e A187177 ..0..5..0..0..0..0....3..0..0..0..0..6....0..0..2..0..0..0....0..0..6..0..0..0
%e A187177 ..0..0..0..0..7..0....0..0..0..5..0..0....1..0..0..0..0..4....7..0..0..0..0..2
%e A187177 ..0..0..6..0..0..0....0..4..0..0..0..0....0..0..0..3..0..0....0..0..0..1..0..0
%Y A187177 Cf. A187172.
%K A187177 nonn
%O A187177 1,6
%A A187177 _R. H. Hardin_, Mar 06 2011