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A207020 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

%I A207020 #10 Jun 17 2018 14:39:47
%S A207020 9,81,252,558,1035,1719,2646,3852,5373,7245,9504,12186,15327,18963,
%T A207020 23130,27864,33201,39177,45828,53190,61299,70191,79902,90468,101925,
%U A207020 114309,127656,142002,157383,173835,191394,210096,229977,251073,273420,297054
%N A207020 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
%C A207020 Column 4 of A207024.
%H A207020 R. H. Hardin, <a href="/A207020/b207020.txt">Table of n, a(n) for n = 1..210</a>
%F A207020 Empirical: a(n) = 6*n^3 + (27/2)*n^2 - (21/2)*n.
%F A207020 Conjectures from _Colin Barker_, Jun 17 2018: (Start)
%F A207020 G.f.: 9*x*(1 + 5*x - 2*x^2) / (1 - x)^4.
%F A207020 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A207020 (End)
%e A207020 Some solutions for n=4:
%e A207020   1 1 1 1      1 0 0 1      1 1 0 0      1 0 1 0      1 0 0 1
%e A207020   1 1 1 1      0 1 0 0      1 1 0 0      1 0 1 0      1 1 0 0
%e A207020   1 1 0 1      0 1 0 0      0 1 0 0      1 0 1 0      1 1 0 0
%e A207020   0 1 0 1      0 1 0 0      0 1 0 0      1 0 1 0      1 1 0 0
%Y A207020 Cf. A207024.
%K A207020 nonn
%O A207020 1,1
%A A207020 _R. H. Hardin_, Feb 14 2012