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A213413 Half the number of n X 3 binary arrays with no 3 X 3 submatrix formed with any three rows and columns equal to J-I. 1

%I

%S 4,32,253,1970,15109,114302,854473,6323090,46390429,337896422,

%T 2446208593,17618827610,126352826149,902840120942,6431323577113,

%U 45694024938530,323937251540269,2292187810495862,16193839911208033,114251845502143850

%N Half the number of n X 3 binary arrays with no 3 X 3 submatrix formed with any three rows and columns equal to J-I.

%C Column 3 of A213418.

%H R. H. Hardin, <a href="/A213413/b213413.txt">Table of n, a(n) for n = 1..210</a>

%F a(n) = (5^n - 3*6^n + 3*7^n)/2.

%F a(n) = 18*a(n-1) - 107*a(n-2) + 210*a(n-3).

%F G.f.: x*(4 - 40*x + 105*x^2) / ((1 - 5*x)*(1 - 6*x)*(1 - 7*x)). - _Colin Barker_, Jul 21 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A213418.

%K nonn

%O 1,1

%A _R. H. Hardin_ and _N. J. A. Sloane_, Jun 10 2012

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Last modified September 17 14:07 EDT 2021. Contains 347478 sequences. (Running on oeis4.)