A187302 - OEIS

%I #10 Apr 23 2018 14:27:36

%S 0,0,108,1368,6264,15596,31172,52256,79634,112568,151266,195512,

%T 245332,300704,361628,428104,500132,577712,660844,749528,843764,

%U 943552,1048892,1159784,1276228,1398224,1525772,1658872,1797524,1941728,2091484,2246792

%N Number of 7-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 Row 7 of A187296.

%H R. H. Hardin, <a href="/A187302/b187302.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 2776*n^2 - 19580*n + 30728 for n>11.

%F Conjectures from _Colin Barker_, Apr 23 2018: (Start)

%F G.f.: 2*x^3*(54 + 522*x + 1242*x^2 + 400*x^3 + 904*x^4 - 368*x^5 + 393*x^6 - 369*x^7 + 104*x^8 - 108*x^9 + 13*x^10 - 11*x^11) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>14.

%F (End)

%e Some solutions for 4 X 4:

%e ..0..0..0..0....0..0..2..1....0..0..0..0....0..2..1..3....0..0..0..0

%e ..5..4..6..0....0..5..7..6....0..4..3..5....0..7..0..0....7..0..0..1

%e ..0..3..2..1....0..4..3..0....1..0..2..0....0..6..5..4....6..5..0..0

%e ..0..0..7..0....0..0..0..0....0..0..7..6....0..0..0..0....0..4..3..2

%Y Cf. A187296.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 08 2011