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A202196 Number of (n+2) X 4 binary arrays avoiding patterns 001 and 101 in rows and columns.

%I A202196 #11 May 27 2018 06:55:33
%S A202196 240,640,1400,2688,4704,7680,11880,17600,25168,34944,47320,62720,
%T A202196 81600,104448,131784,164160,202160,246400,297528,356224,423200,499200,
%U A202196 585000,681408,789264,909440,1042840,1190400,1353088,1531904,1727880,1942080
%N A202196 Number of (n+2) X 4 binary arrays avoiding patterns 001 and 101 in rows and columns.
%C A202196 Column 2 of A202202.
%H A202196 R. H. Hardin, <a href="/A202196/b202196.txt">Table of n, a(n) for n = 1..210</a>
%F A202196 Empirical: a(n) = 4*(n+4)*(n+3)*(n+2)^2/3.
%F A202196 Conjectures from _Colin Barker_, May 27 2018: (Start)
%F A202196 G.f.: 8*x*(30 - 70*x + 75*x^2 - 39*x^3 + 8*x^4) / (1 - x)^5.
%F A202196 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A202196 (End)
%e A202196 Some solutions for n=6:
%e A202196 ..0..1..1..1....1..1..1..1....1..1..1..0....1..1..1..1....1..1..1..1
%e A202196 ..1..1..1..1....1..1..1..0....1..1..1..1....1..1..1..1....1..1..1..1
%e A202196 ..1..1..1..1....1..1..0..0....1..1..1..0....0..1..1..1....1..1..1..1
%e A202196 ..1..1..1..0....1..1..0..0....0..1..1..0....0..1..1..1....1..1..1..1
%e A202196 ..1..1..1..0....1..1..0..0....0..1..1..0....0..1..1..1....1..1..1..1
%e A202196 ..1..1..1..0....1..1..0..0....0..1..0..0....0..1..1..0....0..1..1..1
%e A202196 ..1..1..0..0....1..1..0..0....0..0..0..0....0..1..1..0....0..1..1..0
%e A202196 ..1..1..0..0....1..1..0..0....0..0..0..0....0..1..0..0....0..1..1..0
%Y A202196 Cf. A202202.
%K A202196 nonn
%O A202196 1,1
%A A202196 _R. H. Hardin_, Dec 14 2011