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A250723 Number of (n+1) X (2+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 A250723 #7 Nov 16 2018 06:07:46
%S A250723 22,46,85,144,230,350,513,728,1006,1358,1797,2336,2990,3774,4705,5800,
%T A250723 7078,8558,10261,12208,14422,16926,19745,22904,26430,30350,34693,
%U A250723 39488,44766,50558,56897,63816,71350,79534,88405,98000,108358,119518,131521
%N A250723 Number of (n+1) X (2+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 A250723 R. H. Hardin, <a href="/A250723/b250723.txt">Table of n, a(n) for n = 1..210</a>
%F A250723 Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6).
%F A250723 Empirical for n mod 2 = 0: a(n) = (1/24)*n^4 + (1/2)*n^3 + (10/3)*n^2 + 10*n + 8.
%F A250723 Empirical for n mod 2 = 1: a(n) = (1/24)*n^4 + (1/2)*n^3 + (10/3)*n^2 + 10*n + (65/8).
%F A250723 Empirical g.f.: x*(22 - 42*x + 11*x^2 + 34*x^3 - 31*x^4 + 8*x^5) / ((1 - x)^5*(1 + x)). - _Colin Barker_, Nov 16 2018
%e A250723 Some solutions for n=4:
%e A250723 ..0..0..0....0..1..1....0..0..1....0..0..0....1..0..1....0..0..0....0..0..0
%e A250723 ..0..0..1....1..1..1....0..1..1....0..0..0....0..1..1....0..0..0....0..0..0
%e A250723 ..1..0..1....1..1..1....0..1..1....0..0..0....1..1..1....0..0..0....0..0..0
%e A250723 ..0..1..1....1..1..1....0..1..1....0..0..0....1..1..1....0..0..0....0..0..1
%e A250723 ..0..1..1....1..1..1....1..1..1....0..1..1....1..1..1....1..0..0....0..1..1
%Y A250723 Column 2 of A250729.
%K A250723 nonn
%O A250723 1,1
%A A250723 _R. H. Hardin_, Nov 27 2014