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A208286 Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

%I A208286 #8 Jun 29 2018 14:18:35
%S A208286 42,1764,14946,70216,239490,665892,1604862,3478160,6942474,12974340,
%T A208286 22973082,38883480,63339874,99833412,152904150,228359712,333522218,
%U A208286 477505188,671522130,929228520,1267098882,1704840676,2265846702
%N A208286 Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.
%C A208286 Column 7 of A208287.
%H A208286 R. H. Hardin, <a href="/A208286/b208286.txt">Table of n, a(n) for n = 1..210</a>
%F A208286 Empirical: a(n) = (61/180)*n^7 + (121/20)*n^6 + (1157/36)*n^5 + (425/12)*n^4 - (2923/90)*n^3 - (22/15)*n^2 + 2*n.
%F A208286 Conjectures from _Colin Barker_, Jun 29 2018: (Start)
%F A208286 G.f.: 2*x*(21 + 714*x + 1005*x^2 - 1156*x^3 + 203*x^4 + 86*x^5 - 19*x^6) / (1 - x)^8.
%F A208286 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F A208286 (End)
%e A208286 Some solutions for n=4:
%e A208286 ..1..1..0..1..1..1..0....1..0..1..1..0..1..1....1..0..1..1..1..0..0
%e A208286 ..1..1..1..0..1..1..0....0..1..0..1..1..1..1....0..1..0..1..1..0..1
%e A208286 ..1..1..1..1..1..1..0....1..0..1..1..0..1..1....0..1..1..1..1..0..1
%e A208286 ..1..1..1..0..1..1..0....1..0..1..1..1..1..1....0..1..1..1..1..0..1
%Y A208286 Cf. A208287.
%K A208286 nonn
%O A208286 1,1
%A A208286 _R. H. Hardin_, Feb 25 2012