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A268419 Number of n X 1 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

%I A268419 #10 Jan 13 2019 11:30:22
%S A268419 1,2,5,14,44,147,505,1750,6065,20950,72052,246715,841345,2858714,
%T A268419 9682221,32700942,110173948,370393059,1242869721,4163561358,
%U A268419 13927246329,46526402422,155249799428,517505902283,1723457914689,5734951039346
%N A268419 Number of n X 1 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.
%H A268419 R. H. Hardin, <a href="/A268419/b268419.txt">Table of n, a(n) for n = 1..210</a>
%F A268419 Empirical: a(n) = 8*a(n-1) - 20*a(n-2) + 12*a(n-3) + 12*a(n-4) - 8*a(n-5) - 3*a(n-6).
%F A268419 Empirical g.f.: x*(1 - 6*x + 9*x^2 + 2*x^3 - 4*x^4 - x^5) / ((1 - x)*(1 - 3*x)*(1 - x - x^2)*(1 - 3*x - x^2)). - _Colin Barker_, Jan 13 2019
%e A268419 Some solutions for n=8:
%e A268419 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A268419 ..0....1....1....1....0....1....1....1....1....0....1....1....1....1....0....1
%e A268419 ..0....2....1....2....0....0....1....2....0....1....0....2....0....2....0....0
%e A268419 ..1....2....0....2....0....1....1....1....2....2....2....0....2....1....1....1
%e A268419 ..2....3....2....1....0....2....0....2....3....0....1....0....0....3....0....1
%e A268419 ..0....0....3....0....0....1....1....3....3....2....3....2....3....0....2....1
%e A268419 ..3....2....0....3....0....0....2....3....3....0....1....0....2....2....1....2
%e A268419 ..0....2....3....2....1....3....3....2....1....1....0....2....2....0....0....1
%Y A268419 Column 1 of A268423.
%K A268419 nonn
%O A268419 1,2
%A A268419 _R. H. Hardin_, Feb 04 2016