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%I #8 Nov 28 2018 10:57:45
%S 61,238,890,3369,12859,48980,186162,707897,2693783,10250631,38999597,
%T 148376603,564538287,2147959151,8172471594,31094184171,118305857859,
%U 450125886029,1712621797025,6516115115442,24792258076798,94328620512132
%N Number of (n+1) X (3+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="/A251312/b251312.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-1) - 27*a(n-2) + 64*a(n-3) - 110*a(n-4) + 121*a(n-5) - 91*a(n-6) + 46*a(n-7) - 14*a(n-8) + a(n-9) - a(n-10).
%F Empirical g.f.: x*(61 - 250*x + 633*x^2 - 1229*x^3 + 1415*x^4 - 1090*x^5 + 552*x^6 - 163*x^7 - 2*x^8 - 11*x^9) / (1 - 8*x + 27*x^2 - 64*x^3 + 110*x^4 - 121*x^5 + 91*x^6 - 46*x^7 + 14*x^8 - x^9+ x^10). - _Colin Barker_, Nov 28 2018
%e Some solutions for n=4:
%e ..1..1..1..0....1..1..1..1....0..0..0..1....1..1..1..0....0..1..1..0
%e ..0..0..1..0....0..0..0..1....0..0..0..1....0..0..1..1....0..0..1..1
%e ..0..0..1..1....1..0..0..1....1..0..0..0....1..0..0..0....0..0..0..1
%e ..0..0..0..1....1..0..0..0....1..0..0..0....1..0..0..0....1..0..0..1
%e ..1..1..0..1....1..1..1..0....1..0..0..0....1..1..1..0....1..0..0..1
%Y Column 3 of A251317.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 01 2014
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