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A251125 Number of (n+1) X (5+1) 0..1 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.

%I A251125 #10 Nov 26 2018 06:57:17
%S A251125 125,193,272,401,580,854,1268,1912,2921,4520,7069,11153,17717,28291,
%T A251125 45350,72899,117418,189392,305786,494050,798599,1291298,2088427,
%U A251125 3378131,5464835,8841109,14303948,23142917,37444576,60585050,98027024,158609308
%N A251125 Number of (n+1) X (5+1) 0..1 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.
%H A251125 R. H. Hardin, <a href="/A251125/b251125.txt">Table of n, a(n) for n = 1..210</a>
%F A251125 Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5) for n>6.
%F A251125 Empirical g.f.: x*(125 - 307*x + 125*x^2 + 153*x^3 - 107*x^4 + 6*x^5) / ((1 - x)^3*(1 - x - x^2)). - _Colin Barker_, Nov 26 2018
%e A251125 Some solutions for n=4:
%e A251125 ..0..0..0..0..0..1....0..0..0..0..1..1....0..0..0..1..1..1....0..0..1..0..1..1
%e A251125 ..0..0..0..0..0..1....0..0..0..0..0..0....0..0..0..0..0..0....0..0..1..0..1..0
%e A251125 ..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..1..0..1..0
%e A251125 ..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..1..0..1..0
%e A251125 ..1..1..0..0..0..0....1..1..0..0..0..0....1..1..1..1..1..0....0..0..1..0..1..0
%Y A251125 Column 5 of A251128.
%K A251125 nonn
%O A251125 1,1
%A A251125 _R. H. Hardin_, Nov 30 2014