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A207106 Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.

%I A207106 #11 Feb 22 2018 05:29:13
%S A207106 6,36,98,200,350,556,826,1168,1590,2100,2706,3416,4238,5180,6250,7456,
%T A207106 8806,10308,11970,13800,15806,17996,20378,22960,25750,28756,31986,
%U A207106 35448,39150,43100,47306,51776,56518,61540,66850,72456,78366,84588,91130,98000
%N A207106 Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.
%C A207106 Column 3 of A207111.
%H A207106 R. H. Hardin, <a href="/A207106/b207106.txt">Table of n, a(n) for n = 1..210</a>
%F A207106 Empirical: a(n) = (4/3)*n^3 + 8*n^2 - (10/3)*n.
%F A207106 Conjectures from _Colin Barker_, Feb 20 2018: (Start)
%F A207106 G.f.: 2*x*(3 + 6*x - 5*x^2) / (1 - x)^4.
%F A207106 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A207106 (End)
%e A207106 Some solutions for n=4:
%e A207106 ..1..1..1....0..1..0....1..0..0....1..0..0....1..1..1....0..1..0....1..1..0
%e A207106 ..1..1..1....1..0..1....0..0..1....1..0..1....1..1..0....1..1..0....0..0..1
%e A207106 ..1..1..1....0..0..1....1..0..1....1..0..1....1..1..1....1..1..0....0..1..0
%e A207106 ..1..1..1....1..0..1....0..0..1....1..0..1....1..1..1....1..1..0....0..1..0
%Y A207106 Cf. A207111.
%K A207106 nonn
%O A207106 1,1
%A A207106 _R. H. Hardin_, Feb 15 2012