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A230331 Number of n X 2 0..2 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero. 1

%I #8 Sep 21 2018 14:58:02

%S 0,6,34,218,1386,8810,56010,356074,2263690,14391082,91489226,

%T 581629546,3697625866,23507122602,149443138122,950063174890,

%U 6039889469834,38397725300778,244107994962122,1551881335096170,9865861536380938

%N Number of n X 2 0..2 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

%H R. H. Hardin, <a href="/A230331/b230331.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) + 8*a(n-2) + 4*a(n-3).

%F Empirical g.f.: 2*x^2*(3 + 2*x) / (1 - 5*x - 8*x^2 - 4*x^3). - _Colin Barker_, Sep 21 2018

%e Some solutions for n=3.

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

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

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

%Y Column 2 of A230337.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 16 2013

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