cp's OEIS Frontend

A187156 Number of 3-step one space at a time bishop's tours on an n X n board summed over all starting positions.

%I A187156 #10 Feb 28 2018 10:43:59
%S A187156 0,0,20,64,132,224,340,480,644,832,1044,1280,1540,1824,2132,2464,2820,
%T A187156 3200,3604,4032,4484,4960,5460,5984,6532,7104,7700,8320,8964,9632,
%U A187156 10324,11040,11780,12544,13332,14144,14980,15840,16724,17632,18564,19520,20500
%N A187156 Number of 3-step one space at a time bishop's tours on an n X n board summed over all starting positions.
%C A187156 Row 3 of A187155.
%H A187156 R. H. Hardin, <a href="/A187156/b187156.txt">Table of n, a(n) for n = 1..50</a>
%F A187156 Empirical: a(n) = 12*n^2 - 40*n + 32 for n>1.
%F A187156 Conjectures from _Colin Barker_, Feb 28 2018: (Start)
%F A187156 G.f.: 4*x^3*(5 + x) / (1 - x)^3.
%F A187156 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.
%F A187156 (End)
%e A187156 Some solutions for 4 X 4:
%e A187156 ..0..0..0..3....0..0..3..0....1..0..0..0....0..1..0..3....0..1..0..0
%e A187156 ..0..0..2..0....0..2..0..0....0..2..0..0....0..0..2..0....0..0..2..0
%e A187156 ..0..1..0..0....0..0..1..0....3..0..0..0....0..0..0..0....0..3..0..0
%e A187156 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%Y A187156 Cf. A187155.
%K A187156 nonn
%O A187156 1,3
%A A187156 _R. H. Hardin_, Mar 06 2011