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A251123 Number of (n+1) X (3+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 A251123 #10 Nov 25 2018 11:44:18
%S A251123 40,69,108,173,272,430,680,1080,1721,2752,4413,7093,11421,18415,29722,
%T A251123 48007,77582,125424,202822,328042,530639,858434,1388803,2246943,
%U A251123 3635427,5882025,9517080,15398705,24915356,40313602,65228468,105541548,170769461
%N A251123 Number of (n+1) X (3+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 A251123 R. H. Hardin, <a href="/A251123/b251123.txt">Table of n, a(n) for n = 1..210</a>
%F A251123 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 A251123 Empirical g.f.: x*(40 - 91*x + 32*x^2 + 46*x^3 - 29*x^4 + x^5) / ((1 - x)^3*(1 - x - x^2)). - _Colin Barker_, Nov 25 2018
%e A251123 Some solutions for n=4:
%e A251123 ..1..0..1..1....1..0..0..1....0..0..1..0....0..0..0..1....1..1..1..1
%e A251123 ..1..0..1..0....1..0..0..0....0..0..1..0....1..1..1..1....0..0..0..0
%e A251123 ..1..0..1..0....1..0..0..0....0..0..1..0....0..0..0..0....1..0..0..0
%e A251123 ..1..0..1..0....1..0..0..0....0..0..1..0....0..0..0..0....1..0..0..0
%e A251123 ..1..0..1..0....1..0..0..0....0..0..1..0....1..0..0..0....1..0..0..0
%Y A251123 Column 3 of A251128.
%K A251123 nonn
%O A251123 1,1
%A A251123 _R. H. Hardin_, Nov 30 2014