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A184469 1/6 the number of (n+2) X 3 0..2 arrays with each 3 X 3 subblock containing one of one value, four of another, and four of the last.

%I A184469 #9 Apr 12 2018 12:27:59
%S A184469 315,1095,3705,12339,45585,161739,559305,2147931,7836561,27667251,
%T A184469 108488889,401513355,1432182465,5674143555,21145265865,75792359259,
%U A184469 301775575185,1128283339059,4053433203225,16177609637451,60579025906401
%N A184469 1/6 the number of (n+2) X 3 0..2 arrays with each 3 X 3 subblock containing one of one value, four of another, and four of the last.
%C A184469 Column 1 of A184477.
%H A184469 R. H. Hardin, <a href="/A184469/b184469.txt">Table of n, a(n) for n = 1..200</a>
%F A184469 Empirical: a(n) = 3*a(n-1) + 96*a(n-3) - 288*a(n-4) - 2700*a(n-6) + 8100*a(n-7) + 23328*a(n-9) - 69984*a(n-10).
%F A184469 Empirical g.f.: 3*x*(105 + 50*x + 140*x^2 - 9672*x^3 - 1944*x^4 - 5112*x^5 + 269028*x^6 + 17496*x^7 + 42768*x^8 - 2332800*x^9) / ((1 - 3*x)*(1 - 18*x^3)*(1 - 24*x^3)*(1 - 54*x^3)). - _Colin Barker_, Apr 12 2018
%e A184469 Some solutions with a(1,1)=0 for 4 X 3:
%e A184469 ..0..2..2....0..1..2....0..2..0....0..0..2....0..1..2....0..1..2....0..2..1
%e A184469 ..2..0..1....1..2..1....0..2..0....2..0..2....1..2..1....0..2..0....1..1..2
%e A184469 ..0..2..0....2..1..2....2..1..2....2..1..0....2..1..2....2..2..0....1..2..2
%e A184469 ..0..2..2....2..0..1....0..2..0....0..0..2....1..0..2....0..1..2....2..0..1
%Y A184469 Cf. A184477.
%K A184469 nonn
%O A184469 1,1
%A A184469 _R. H. Hardin_, Jan 15 2011