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A250724 Number of (n+1) X (3+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 A250724 #7 Nov 16 2018 06:10:57
%S A250724 50,110,208,365,600,942,1418,2065,2918,4022,5420,7165,9308,11910,
%T A250724 15030,18737,23098,28190,34088,40877,48640,57470,67458,78705,91310,
%U A250724 105382,121028,138365,157508,178582,201710,227025,254658,284750,317440,352877
%N A250724 Number of (n+1) X (3+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 A250724 R. H. Hardin, <a href="/A250724/b250724.txt">Table of n, a(n) for n = 1..210</a>
%F A250724 Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6).
%F A250724 Empirical for n mod 2 = 0: a(n) = (1/6)*n^4 + (4/3)*n^3 + (91/12)*n^2 + (74/3)*n + 17.
%F A250724 Empirical for n mod 2 = 1: a(n) = (1/6)*n^4 + (4/3)*n^3 + (91/12)*n^2 + (74/3)*n + (65/4).
%F A250724 Empirical g.f.: x*(50 - 90*x + 18*x^2 + 83*x^3 - 70*x^4 + 17*x^5) / ((1 - x)^5*(1 + x)). - _Colin Barker_, Nov 16 2018
%e A250724 Some solutions for n=4:
%e A250724 ..0..0..0..1....0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..0
%e A250724 ..0..0..0..1....0..0..1..1....0..0..0..0....0..1..1..1....0..0..0..1
%e A250724 ..0..1..1..1....0..0..1..1....0..0..0..1....0..1..1..1....0..1..1..1
%e A250724 ..1..1..1..1....0..0..1..1....0..0..0..1....0..1..1..1....1..1..1..1
%e A250724 ..1..1..1..1....1..0..1..1....0..0..0..1....1..1..1..1....1..1..1..1
%Y A250724 Column 3 of A250729.
%K A250724 nonn
%O A250724 1,1
%A A250724 _R. H. Hardin_, Nov 27 2014