cp's OEIS Frontend

A207596 Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.

%I A207596 #8 Jun 25 2018 06:08:36
%S A207596 15,225,825,1995,3915,6765,10725,15975,22695,31065,41265,53475,67875,
%T A207596 84645,103965,126015,150975,179025,210345,245115,283515,325725,371925,
%U A207596 422295,477015,536265,600225,669075,742995,822165,906765,996975,1092975
%N A207596 Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
%C A207596 Column 5 of A207599.
%H A207596 R. H. Hardin, <a href="/A207596/b207596.txt">Table of n, a(n) for n = 1..210</a>
%F A207596 Empirical: a(n) = 30*n^3 + 15*n^2 - 45*n + 15.
%F A207596 Conjectures from _Colin Barker_, Jun 25 2018: (Start)
%F A207596 G.f.: 15*x*(1 + 11*x + x^2 - x^3) / (1 - x)^4.
%F A207596 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A207596 (End)
%e A207596 Some solutions for n=4:
%e A207596 ..1..1..0..0..1....0..1..1..0..1....1..0..1..1..0....0..1..1..1..1
%e A207596 ..1..0..1..1..0....1..0..1..1..0....1..0..1..1..1....1..0..1..1..1
%e A207596 ..0..0..1..1..0....0..0..1..1..0....0..0..1..1..1....0..0..1..1..0
%e A207596 ..0..0..1..1..0....0..0..1..1..0....0..0..1..1..0....0..0..1..1..0
%Y A207596 Cf. A207599.
%K A207596 nonn
%O A207596 1,1
%A A207596 _R. H. Hardin_, Feb 19 2012