cp's OEIS Frontend

A187159 Number of 6-step one space at a time bishop's tours on an n X n board summed over all starting positions.

%I A187159 #10 Apr 20 2018 09:44:27
%S A187159 0,0,0,56,456,1588,3288,5556,8392,11796,15768,20308,25416,31092,37336,
%T A187159 44148,51528,59476,67992,77076,86728,96948,107736,119092,131016,
%U A187159 143508,156568,170196,184392,199156,214488,230388,246856,263892,281496,299668
%N A187159 Number of 6-step one space at a time bishop's tours on an n X n board summed over all starting positions.
%C A187159 Row 6 of A187155.
%H A187159 R. H. Hardin, <a href="/A187159/b187159.txt">Table of n, a(n) for n = 1..50</a>
%F A187159 Empirical: a(n) = 284*n^2 - 1992*n + 3316 for n>4.
%F A187159 Conjectures from _Colin Barker_, Apr 20 2018: (Start)
%F A187159 G.f.: 4*x^4*(14 + 72*x + 97*x^2 - 41*x^3) / (1 - x)^3.
%F A187159 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
%F A187159 (End)
%e A187159 Some solutions for 4 X 4:
%e A187159 ..0..3..0..0....0..0..2..0....0..0..5..0....0..0..4..0....0..3..0..0
%e A187159 ..4..0..2..0....0..1..0..3....0..4..0..6....0..5..0..3....2..0..4..0
%e A187159 ..0..5..0..1....6..0..4..0....3..0..1..0....6..0..2..0....0..1..0..5
%e A187159 ..0..0..6..0....0..5..0..0....0..2..0..0....0..1..0..0....0..0..6..0
%Y A187159 Cf. A187155.
%K A187159 nonn
%O A187159 1,4
%A A187159 _R. H. Hardin_, Mar 06 2011