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Number of (n+1) X (2+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.
1

%I #8 Dec 31 2018 11:27:51

%S 0,4,12,48,144,468,1404,4320,12960,39204,117612,353808,1061424,

%T 3187188,9561564,28693440,86080320,258267204,774801612,2324483568,

%U 6973450704,20920588308,62761764924,188286003360,564858010080,1694576156004

%N Number of (n+1) X (2+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

%H R. H. Hardin, <a href="/A262414/b262414.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 3*a(n-2) - 9*a(n-3).

%F Empirical g.f.: 4*x^2 / ((1 - 3*x)*(1 - 3*x^2)). - _Colin Barker_, Dec 31 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 2 of A262420.

%K nonn

%O 1,2

%A _R. H. Hardin_, Sep 22 2015