cp's OEIS Frontend

A187158 Number of 5-step one space at a time bishop's tours on an n X n board summed over all starting positions.

%I A187158 #10 Apr 20 2018 09:27:59
%S A187158 0,0,0,72,388,904,1620,2536,3652,4968,6484,8200,10116,12232,14548,
%T A187158 17064,19780,22696,25812,29128,32644,36360,40276,44392,48708,53224,
%U A187158 57940,62856,67972,73288,78804,84520,90436,96552,102868,109384,116100,123016,130132
%N A187158 Number of 5-step one space at a time bishop's tours on an n X n board summed over all starting positions.
%C A187158 Row 5 of A187155.
%H A187158 R. H. Hardin, <a href="/A187158/b187158.txt">Table of n, a(n) for n = 1..50</a>
%F A187158 Empirical: a(n) = 100*n^2 - 584*n + 808 for n>3.
%F A187158 Conjectures from _Colin Barker_, Apr 20 2018: (Start)
%F A187158 G.f.: 4*x^4*(18 + 43*x - 11*x^2) / (1 - x)^3.
%F A187158 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
%F A187158 (End)
%e A187158 Some solutions for 4 X 4:
%e A187158 ..0..0..1..0....0..4..0..0....0..0..0..0....0..5..0..1....0..2..0..0
%e A187158 ..0..2..0..0....3..0..5..0....0..3..0..5....4..0..2..0....3..0..1..0
%e A187158 ..5..0..3..0....0..2..0..0....2..0..4..0....0..3..0..0....0..4..0..0
%e A187158 ..0..4..0..0....0..0..1..0....0..1..0..0....0..0..0..0....0..0..5..0
%Y A187158 Cf. A187155.
%K A187158 nonn
%O A187158 1,4
%A A187158 _R. H. Hardin_, Mar 06 2011