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A208285 Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

%I A208285 #8 Jun 29 2018 15:24:05
%S A208285 26,676,4374,16872,49130,119580,256774,502416,914778,1572500,2578774,
%T A208285 4065912,6200298,9187724,13279110,18776608,26040090,35494020,47634710,
%U A208285 63037960,82367082,106381308,135944582,172034736,215753050,268334196
%N A208285 Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.
%C A208285 Column 6 of A208287.
%H A208285 R. H. Hardin, <a href="/A208285/b208285.txt">Table of n, a(n) for n = 1..210</a>
%F A208285 Empirical: a(n) = (8/15)*n^6 + (23/3)*n^5 + (82/3)*n^4 + (1/3)*n^3 - (178/15)*n^2 + 2*n.
%F A208285 Conjectures from _Colin Barker_, Jun 29 2018: (Start)
%F A208285 G.f.: 2*x*(13 + 247*x + 94*x^2 - 230*x^3 + 65*x^4 + 3*x^5) / (1 - x)^7.
%F A208285 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A208285 (End)
%e A208285 Some solutions for n=4:
%e A208285 ..0..1..0..1..1..0....0..1..1..1..1..0....1..1..1..1..0..0....1..0..1..0..1..0
%e A208285 ..0..1..0..1..0..1....1..0..1..1..0..1....1..1..0..1..1..1....0..1..0..1..0..1
%e A208285 ..0..1..0..1..0..0....0..1..1..1..1..0....1..1..1..1..0..0....1..0..1..0..1..0
%e A208285 ..0..1..0..1..0..0....1..1..1..1..0..1....1..1..0..1..1..0....1..0..1..1..1..1
%Y A208285 Cf. A208287.
%K A208285 nonn
%O A208285 1,1
%A A208285 _R. H. Hardin_, Feb 25 2012