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A204699 Number of n X 2 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.

%I A204699 #8 Feb 23 2018 09:51:35
%S A204699 2,14,96,726,5400,40344,301056,2247264,16773504,125199744,934502400,
%T A204699 6975223296,52063770624,388609284096,2900619165696,21650516238336,
%U A204699 161601653145600,1206211160408064,9003282670288896,67201416721465344
%N A204699 Number of n X 2 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.
%C A204699 Column 2 of A204705.
%H A204699 R. H. Hardin, <a href="/A204699/b204699.txt">Table of n, a(n) for n = 1..210</a>
%F A204699 Empirical: a(n) = 6*a(n-1) + 12*a(n-2) - 8*a(n-3) for n>5.
%F A204699 Empirical g.f.: 2*x*(1 - 2*x)*(1 + 3*x - x^3) / ((1 + 2*x)*(1 - 8*x + 4*x^2)). - _Colin Barker_, Feb 23 2018
%e A204699 Some solutions for n=5:
%e A204699 ..0..0....0..0....0..1....0..1....0..1....0..1....0..0....0..1....0..0....0..1
%e A204699 ..0..1....0..1....1..1....2..0....2..0....0..2....0..1....0..2....1..2....0..0
%e A204699 ..2..0....2..1....0..2....0..1....1..2....2..0....2..0....1..1....0..2....2..0
%e A204699 ..1..2....2..2....2..2....2..2....2..0....0..2....1..0....1..2....1..0....0..2
%e A204699 ..0..2....0..0....1..0....2..1....0..1....1..0....0..2....2..1....2..1....0..0
%Y A204699 Cf. A204705.
%K A204699 nonn
%O A204699 1,1
%A A204699 _R. H. Hardin_, Jan 18 2012