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A208378 Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

%I A208378 #8 Jul 02 2018 08:37:36
%S A208378 42,1764,6216,13860,25200,40740,60984,86436,117600,154980,199080,
%T A208378 250404,309456,376740,452760,538020,633024,738276,854280,981540,
%U A208378 1120560,1271844,1435896,1613220,1804320,2009700,2229864,2465316,2716560,2984100,3268440
%N A208378 Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
%C A208378 Column 7 of A208379.
%H A208378 R. H. Hardin, <a href="/A208378/b208378.txt">Table of n, a(n) for n = 1..210</a>
%F A208378 Empirical: a(n) = 84*n^3 + 840*n^2 - 1344*n + 420 for n>1.
%F A208378 Conjectures from _Colin Barker_, Jul 02 2018: (Start)
%F A208378 G.f.: 42*x*(1 + 38*x - 14*x^2 - 14*x^3 + x^4) / (1 - x)^4.
%F A208378 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.
%F A208378 (End)
%e A208378 Some solutions for n=4:
%e A208378 ..1..1..0..1..0..0..1....0..1..0..1..0..0..1....1..0..1..1..0..0..1
%e A208378 ..1..1..0..0..1..1..0....0..1..1..0..1..1..0....1..1..0..0..1..1..0
%e A208378 ..1..1..0..0..1..1..0....0..1..1..0..0..1..0....0..1..0..0..1..1..0
%e A208378 ..0..1..0..0..1..0..0....0..0..1..0..0..1..0....0..1..0..0..1..0..0
%Y A208378 Cf. A208379.
%K A208378 nonn
%O A208378 1,1
%A A208378 _R. H. Hardin_, Feb 25 2012