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A250725 Number of (n+1) X (4+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 A250725 #7 Nov 16 2018 07:51:10
%S A250725 114,257,496,885,1500,2434,3807,5760,8465,12119,16954,23231,31250,
%T A250725 41344,53889,69298,88031,110589,137524,169433,206968,250830,301779,
%U A250725 360628,428253,505587,593630,693443,806158,932972,1075157,1234054,1411083
%N A250725 Number of (n+1) X (4+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 A250725 R. H. Hardin, <a href="/A250725/b250725.txt">Table of n, a(n) for n = 1..210</a>
%F A250725 Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 5*a(n-3) + 5*a(n-4) - 9*a(n-5) + 5*a(n-6) - a(n-7) for n>8.
%F A250725 Empirical for n mod 2 = 0: a(n) = (1/60)*n^5 + (13/24)*n^4 + (8/3)*n^3 + (407/24)*n^2 + (3859/60)*n + 30 for n>1.
%F A250725 Empirical for n mod 2 = 1: a(n) = (1/60)*n^5 + (13/24)*n^4 + (8/3)*n^3 + (407/24)*n^2 + (3859/60)*n + (61/2) for n>1.
%F A250725 Empirical g.f.: x*(114 - 313*x + 237*x^2 + 148*x^3 - 316*x^4 + 160*x^5 - 25*x^6 - x^7) / ((1 - x)^6*(1 + x)). - _Colin Barker_, Nov 16 2018
%e A250725 Some solutions for n=4:
%e A250725 ..0..0..0..1..1....0..0..0..0..0....0..0..0..1..1....0..0..0..0..0
%e A250725 ..0..0..0..1..1....0..1..0..0..1....0..0..0..1..1....1..0..0..0..0
%e A250725 ..0..0..0..1..1....1..0..1..1..1....0..0..0..1..1....0..1..0..0..0
%e A250725 ..1..1..1..1..1....0..1..1..1..1....0..0..0..1..1....1..0..1..0..0
%e A250725 ..1..1..1..1..1....1..1..1..1..1....0..1..1..1..1....0..1..0..1..1
%Y A250725 Column 4 of A250729.
%K A250725 nonn
%O A250725 1,1
%A A250725 _R. H. Hardin_, Nov 27 2014