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Number of (n+2) X 6 0..2 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..2 introduced in row major order.
1

%I #8 Jun 06 2018 18:55:33

%S 1758,193,256,244,442,982,1914,4922,13138,34498,93778,255730,696018,

%T 1900754,5192146,14180050,38739154,105835858,289138770,789939026,

%U 2158150738,5896157266,16108595794,44009496658,120236140626,328491234386

%N Number of (n+2) X 6 0..2 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..2 introduced in row major order.

%C Column 4 of A204284.

%H R. H. Hardin, <a href="/A204280/b204280.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -6*a(n-4) +4*a(n-6) for n>8.

%F Empirical g.f.: x*(1758 - 5081*x - 323*x^2 - 524*x^3 + 10258*x^4 + 814*x^5 - 6528*x^6 - 128*x^7) / ((1 - x)*(1 - 2*x - 2*x^2)*(1 - 2*x^3)). - _Colin Barker_, Jun 06 2018

%e Some solutions for n=4:

%e ..0..1..0..0..2..0....0..0..0..0..0..0....0..1..0..1..1..0....0..1..0..2..0..1

%e ..0..1..0..0..2..0....0..0..0..0..0..0....0..1..0..1..1..0....0..1..0..2..0..1

%e ..0..1..0..0..2..0....1..1..1..1..1..1....0..1..0..1..1..0....0..1..0..2..0..1

%e ..0..1..0..0..2..0....2..2..2..2..2..2....0..1..0..1..1..0....0..1..0..2..0..1

%e ..0..1..0..0..2..0....1..1..1..1..1..1....0..1..0..1..1..0....0..1..0..2..0..1

%e ..0..1..0..0..2..0....2..2..2..2..2..2....0..1..0..1..1..0....0..1..0..2..0..1

%Y Cf. A204284.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 13 2012