A187177 - OEIS

%I #13 Apr 22 2018 17:47:40

%S 0,0,0,0,0,16,368,1600,4284,8760,15104,23144,32764,43944,56684,70984,

%T 86844,104264,123244,143784,165884,189544,214764,241544,269884,299784,

%U 331244,364264,398844,434984,472684,511944,552764,595144,639084,684584

%N 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 Row 7 of A187172.

%H R. H. Hardin, <a href="/A187177/b187177.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 780*n^2 - 9880*n + 29384 for n>11.

%F 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 Some solutions for 6 X 6:

%e ..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 ..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 ..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 ..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 ..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 ..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 Cf. A187172.

%K nonn

%O 1,6

%A _R. H. Hardin_, Mar 06 2011