cp's OEIS Frontend

A187160 Number of 7-step one space at a time bishop's tours on an n X n board summed over all starting positions.

%I A187160 #10 Apr 20 2018 10:05:22
%S A187160 0,0,0,16,544,2328,6172,11576,18540,27064,37148,48792,61996,76760,
%T A187160 93084,110968,130412,151416,173980,198104,223788,251032,279836,310200,
%U A187160 342124,375608,410652,447256,485420,525144,566428,609272,653676,699640,747164
%N A187160 Number of 7-step one space at a time bishop's tours on an n X n board summed over all starting positions.
%C A187160 Row 7 of A187155.
%H A187160 R. H. Hardin, <a href="/A187160/b187160.txt">Table of n, a(n) for n = 1..50</a>
%F A187160 Empirical: a(n) = 780*n^2 - 6296*n + 12024 for n>5.
%F A187160 Conjectures from _Colin Barker_, Apr 20 2018: (Start)
%F A187160 G.f.: 4*x^4*(4 + 124*x + 186*x^2 + 201*x^3 - 125*x^4) / (1 - x)^3.
%F A187160 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
%F A187160 (End)
%e A187160 Some solutions for 4 X 4:
%e A187160 ..0..0..4..0....0..7..0..1....7..0..5..0....0..2..0..0....0..0..6..0
%e A187160 ..0..3..0..5....6..0..2..0....0..6..0..4....1..0..3..0....0..5..0..7
%e A187160 ..2..0..6..0....0..5..0..3....1..0..3..0....0..6..0..4....4..0..2..0
%e A187160 ..0..1..0..7....0..0..4..0....0..2..0..0....7..0..5..0....0..3..0..1
%Y A187160 Cf. A187155.
%K A187160 nonn
%O A187160 1,4
%A A187160 _R. H. Hardin_, Mar 06 2011