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A208138 Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

%I A208138 #8 Jun 28 2018 09:37:39
%S A208138 9,81,324,900,2025,3969,7056,11664,18225,27225,39204,54756,74529,
%T A208138 99225,129600,166464,210681,263169,324900,396900,480249,576081,685584,
%U A208138 810000,950625,1108809,1285956,1483524,1703025,1946025,2214144,2509056,2832489
%N A208138 Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
%C A208138 Column 4 of A208142.
%H A208138 R. H. Hardin, <a href="/A208138/b208138.txt">Table of n, a(n) for n = 1..210</a>
%F A208138 Empirical: a(n) = (9/4)*n^4 + (9/2)*n^3 + (9/4)*n^2.
%F A208138 Conjectures from _Colin Barker_, Jun 28 2018: (Start)
%F A208138 G.f.: 9*x*(1 + 4*x + x^2) / (1 - x)^5.
%F A208138 a(n) = 9*(n^2*(1+n)^2) / 4.
%F A208138 (End)
%e A208138 Some solutions for n=4:
%e A208138 ..0..0..0..0....0..1..0..1....1..1..0..1....0..0..0..0....1..0..0..0
%e A208138 ..0..1..0..0....0..0..0..0....1..0..1..0....1..0..0..0....0..1..0..0
%e A208138 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A208138 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%Y A208138 Cf. A208142.
%K A208138 nonn
%O A208138 1,1
%A A208138 _R. H. Hardin_, Feb 23 2012