cp's OEIS Frontend

A187157 Number of 4-step one space at a time bishop's tours on an n X n board summed over all starting positions.

%I A187157 #10 Apr 20 2018 09:28:07
%S A187157 0,0,8,92,248,476,776,1148,1592,2108,2696,3356,4088,4892,5768,6716,
%T A187157 7736,8828,9992,11228,12536,13916,15368,16892,18488,20156,21896,23708,
%U A187157 25592,27548,29576,31676,33848,36092,38408,40796,43256,45788,48392,51068,53816
%N A187157 Number of 4-step one space at a time bishop's tours on an n X n board summed over all starting positions.
%C A187157 Row 4 of A187155.
%H A187157 R. H. Hardin, <a href="/A187157/b187157.txt">Table of n, a(n) for n = 1..50</a>
%F A187157 Empirical: a(n) = 36*n^2 - 168*n + 188 for n>2.
%F A187157 Conjectures from _Colin Barker_, Apr 20 2018: (Start)
%F A187157 G.f.: 4*x^3*(2 + 17*x - x^2) / (1 - x)^3.
%F A187157 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.
%F A187157 (End)
%e A187157 Some solutions for 4 X 4:
%e A187157 ..0..0..4..0....0..0..0..0....0..0..0..0....0..0..4..0....0..4..0..0
%e A187157 ..0..3..0..1....0..0..2..0....0..0..4..0....0..3..0..0....3..0..1..0
%e A187157 ..0..0..2..0....0..3..0..1....0..3..0..1....0..0..2..0....0..2..0..0
%e A187157 ..0..0..0..0....4..0..0..0....0..0..2..0....0..0..0..1....0..0..0..0
%Y A187157 Cf. A187155.
%K A187157 nonn
%O A187157 1,3
%A A187157 _R. H. Hardin_, Mar 06 2011