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A251124 Number of (n+1) X (4+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 A251124 #9 Nov 26 2018 05:30:06
%S A251124 72,117,173,266,401,612,938,1452,2266,3565,5646,8991,14379,23071,
%T A251124 37107,59788,96455,155750,251656,406798,657784,1063847,1720828,
%U A251124 2783801,4503681,7286457,11789033,19074302,30862061,49935000,80795606,130729056
%N A251124 Number of (n+1) X (4+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 A251124 R. H. Hardin, <a href="/A251124/b251124.txt">Table of n, a(n) for n = 1..210</a>
%F A251124 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 A251124 Empirical g.f.: x*(72 - 171*x + 65*x^2 + 87*x^3 - 59*x^4 + 3*x^5) / ((1 - x)^3*(1 - x - x^2)). - _Colin Barker_, Nov 26 2018
%e A251124 Some solutions for n=4:
%e A251124 ..0..0..0..1..0....0..0..0..0..0....0..0..1..0..0....0..0..0..0..1
%e A251124 ..1..0..0..1..0....0..0..0..0..0....0..0..1..0..0....0..0..0..0..1
%e A251124 ..1..0..0..1..0....0..0..0..0..0....0..0..1..0..0....0..0..0..0..1
%e A251124 ..1..0..0..1..0....0..0..0..0..0....1..0..1..0..0....0..0..0..0..1
%e A251124 ..1..0..0..1..0....1..1..1..0..0....1..0..1..0..0....1..0..0..0..1
%Y A251124 Column 4 of A251128.
%K A251124 nonn
%O A251124 1,1
%A A251124 _R. H. Hardin_, Nov 30 2014