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A250734 Number of (5+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

%I A250734 #7 Nov 16 2018 13:52:05
%S A250734 99,230,600,1500,3605,8514,19887,46315,107565,249853,579962,1346953,
%T A250734 3127694,7265717,16877299,39213972,91109305,211714501,491957956,
%U A250734 1143254321,2656749170,6174181500,14348397804,33345661179,77494714919
%N A250734 Number of (5+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
%H A250734 R. H. Hardin, <a href="/A250734/b250734.txt">Table of n, a(n) for n = 1..210</a>
%F A250734 Empirical: a(n) = 4*a(n-1) - 17*a(n-3) + 17*a(n-4) + 12*a(n-5) - 23*a(n-6) + 6*a(n-7) + 3*a(n-8) - a(n-9) for n>12.
%F A250734 Empirical g.f.: x*(99 - 166*x - 320*x^2 + 783*x^3 - 168*x^4 - 804*x^5 + 648*x^6 + 48*x^7 - 119*x^8 - 17*x^9 + 3*x^10 + 3*x^11) / ((1 - x)^3*(1 - x - 6*x^2 + 3*x^3 + 9*x^4 - x^6)). - _Colin Barker_, Nov 16 2018
%e A250734 Some solutions for n=4:
%e A250734 ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....1..0..0..0..0
%e A250734 ..0..0..0..0..1....0..0..0..0..1....0..0..0..0..0....0..1..0..0..0
%e A250734 ..0..0..0..0..1....1..0..0..1..1....0..0..0..1..0....1..0..1..0..0
%e A250734 ..0..0..0..0..1....0..1..1..1..1....1..0..1..0..1....0..1..0..1..1
%e A250734 ..0..0..0..1..1....0..1..1..1..1....0..1..0..1..1....1..0..1..1..1
%e A250734 ..0..1..0..1..1....0..1..1..1..1....1..0..1..1..1....0..1..1..1..1
%Y A250734 Row 5 of A250729.
%K A250734 nonn
%O A250734 1,1
%A A250734 _R. H. Hardin_, Nov 27 2014