A187611 - OEIS

%I #11 Apr 25 2018 11:48:56

%S 0,0,0,0,48,616,2936,8530,17611,32086,51955,76258,105978,140386,

%T 179482,223266,271738,324898,382746,445282,512506,584418,661018,

%U 742306,828282,918946,1014298,1114338,1219066,1328482,1442586,1561378,1684858,1813026

%N Number of 7-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-bishop's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

%C Row 7 of A187606.

%H R. H. Hardin, <a href="/A187611/b187611.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 2344*n^2 - 28880*n + 85282 for n>11.

%F Conjectures from _Colin Barker_, Apr 25 2018: (Start)

%F G.f.: x^5*(48 + 472*x + 1232*x^2 + 1522*x^3 + 213*x^4 + 1907*x^5 - 960*x^7 + 983*x^8 - 729*x^9) / (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 5 X 5:

%e ..0..0..5..0..0....0..0..2..0..0....0..4..0..0..0....0..0..2..0..0

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

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

%e ..0..0..2..0..0....0..0..5..0..0....0..7..0..0..1....0..0..5..0..0

%e ..0..0..0..7..0....0..0..0..7..0....0..0..6..0..0....0..0..0..4..0

%Y Cf. A187606.

%K nonn

%O 1,5

%A _R. H. Hardin_, Mar 11 2011