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A208068 Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

%I A208068 #8 Jun 27 2018 09:07:00
%S A208068 42,1764,6216,21904,48840,108900,198000,360000,582000,940900,1408440,
%T A208068 2108304,2988216,4235364,5762400,7840000,10332000,13616100,17490600,
%U A208068 22467600,28259880,35545444,43928016,54287424,66090960,80460900,96696600
%N A208068 Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.
%C A208068 Column 7 of A208069.
%H A208068 R. H. Hardin, <a href="/A208068/b208068.txt">Table of n, a(n) for n = 1..210</a>
%F A208068 Empirical: a(n) = 2*a(n-1) + 4*a(n-2) - 10*a(n-3) - 5*a(n-4) + 20*a(n-5) - 20*a(n-7) + 5*a(n-8) + 10*a(n-9) - 4*a(n-10) - 2*a(n-11) + a(n-12) for n>13.
%F A208068 Empirical g.f.: 2*x*(21 + 840*x + 1260*x^2 + 1418*x^3 - 991*x^4 - 3128*x^5 - 160*x^6 + 1420*x^7 + 95*x^8 - 160*x^9 + 84*x^10 + 42*x^11 - 21*x^12) / ((1 - x)^7*(1 + x)^5). - _Colin Barker_, Jun 27 2018
%e A208068 Some solutions for n=4:
%e A208068 ..1..1..0..0..1..1..0....1..0..1..0..1..0..1....0..0..1..0..1..1..0
%e A208068 ..0..1..1..0..1..1..0....0..1..0..1..1..0..1....0..0..1..1..0..1..1
%e A208068 ..0..1..0..0..1..1..0....0..0..1..0..1..0..1....0..0..1..0..0..1..0
%e A208068 ..0..0..1..0..0..1..0....0..1..0..1..1..0..0....0..0..1..0..0..1..0
%Y A208068 Cf. A208069.
%K A208068 nonn
%O A208068 1,1
%A A208068 _R. H. Hardin_, Feb 23 2012