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Number of (n+1) X (1+1) 0..1 arrays with no 2 X 2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements.
1

%I #8 Nov 28 2018 10:57:51

%S 10,25,61,149,365,894,2189,5360,13125,32139,78698,192706,471875,

%T 1155470,2829374,6928226,16964995,41541811,101722521,249085705,

%U 609930700,1493523921,3657159252,8955205609,21928415465,53695629760,131483310316

%N Number of (n+1) X (1+1) 0..1 arrays with no 2 X 2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

%H R. H. Hardin, <a href="/A251310/b251310.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(10 - 5*x + 6*x^2 - 4*x^3) / (1 - 3*x + 2*x^2 - 2*x^3 + x^4). - _Colin Barker_, Nov 28 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A251317.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 01 2014