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A208403 Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

%I A208403 #13 Jul 02 2018 10:07:36
%S A208403 5,182,10682,667478,42012698,2646531062,166729574522,10503950018198,
%T A208403 661748758909658,41690171165650742,2626480778916392762,
%U A208403 165468289040095516118,10424502209304556920218,656743639184636861807222
%N A208403 Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.
%C A208403 Column 3 of A208408.
%H A208403 R. H. Hardin, <a href="/A208403/b208403.txt">Table of n, a(n) for n = 1..210</a>
%F A208403 Empirical: a(n) = 70*a(n-1) - 441*a(n-2) for n>3.
%F A208403 Conjectures from _Colin Barker_, Jul 02 2018: (Start)
%F A208403 G.f.: x*(5 - 168*x + 147*x^2) / ((1 - 7*x)*(1 - 63*x)).
%F A208403 a(n) = (2/27)*7^(-1+n) * (27+4*9^n) for n>1.
%F A208403 (End)
%e A208403 Some solutions for n=4:
%e A208403 ..0..0..0....0..0..0....0..0..0....0..0..0....0..1..1....0..0..0....0..0..0
%e A208403 ..1..1..0....0..1..0....0..1..1....0..1..0....1..0..2....0..1..0....0..1..1
%e A208403 ..0..1..0....1..2..1....1..0..0....0..1..1....3..0..1....2..1..1....2..0..2
%e A208403 ..0..1..0....0..1..3....0..1..1....2..0..2....1..1..1....2..1..1....2..1..0
%Y A208403 Cf. A208408.
%K A208403 nonn
%O A208403 1,1
%A A208403 _R. H. Hardin_, Feb 26 2012