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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.
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%I #10 Nov 25 2018 11:44:18

%S 40,69,108,173,272,430,680,1080,1721,2752,4413,7093,11421,18415,29722,

%T 48007,77582,125424,202822,328042,530639,858434,1388803,2246943,

%U 3635427,5882025,9517080,15398705,24915356,40313602,65228468,105541548,170769461

%N 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 R. H. Hardin, <a href="/A251123/b251123.txt">Table of n, a(n) for n = 1..210</a>

%F 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 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 Some solutions for n=4:

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

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

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

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

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

%Y Column 3 of A251128.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 30 2014