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A208140 Number of n X 6 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

%I A208140 #8 Jun 28 2018 14:35:49
%S A208140 16,256,1600,6400,19600,50176,112896,230400,435600,774400,1308736,
%T A208140 2119936,3312400,5017600,7398400,10653696,15023376,20793600,28302400,
%U A208140 37945600,50183056,65545216,84640000,108160000,136890000,171714816
%N A208140 Number of n X 6 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
%C A208140 Column 6 of A208142.
%H A208140 R. H. Hardin, <a href="/A208140/b208140.txt">Table of n, a(n) for n = 1..210</a>
%F A208140 Empirical: a(n) = (4/9)*n^6 + (8/3)*n^5 + (52/9)*n^4 + (16/3)*n^3 + (16/9)*n^2.
%F A208140 Conjectures from _Colin Barker_, Jun 28 2018: (Start)
%F A208140 G.f.: 16*x*(1 + x)*(1 + 8*x + x^2) / (1 - x)^7.
%F A208140 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 A208140 (End)
%e A208140 Some solutions for n=4:
%e A208140 ..0..0..0..0..0..0....1..0..0..0..0..0....1..0..1..0..1..0....1..1..1..1..1..0
%e A208140 ..1..0..1..0..1..0....0..0..0..0..0..0....0..1..0..0..0..0....0..0..0..0..0..0
%e A208140 ..0..0..0..0..0..0....0..0..0..0..0..0....0..1..0..0..0..0....0..0..0..0..0..0
%e A208140 ..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
%Y A208140 Cf. A208142.
%K A208140 nonn
%O A208140 1,1
%A A208140 _R. H. Hardin_, Feb 23 2012