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A250731 Number of (2+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 A250731 #7 Nov 16 2018 10:57:24
%S A250731 18,46,110,257,596,1376,3173,7310,16838,38777,89300,205640,473549,
%T A250731 1090478,2511134,5782577,13315988,30663728,70611701,162602894,
%U A250731 374438006,862246697,1985560724,4572300824,10528983005,24245885486,55832834510
%N A250731 Number of (2+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 A250731 R. H. Hardin, <a href="/A250731/b250731.txt">Table of n, a(n) for n = 1..210</a>
%F A250731 Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 3*a(n-3) for n>4.
%F A250731 Empirical g.f.: x*(18 + 10*x - 18*x^2 - x^3) / ((1 - x)*(1 - x - 3*x^2)). - _Colin Barker_, Nov 16 2018
%e A250731 Some solutions for n=4:
%e A250731 ..0..0..0..0..1....0..0..0..0..1....0..0..0..0..0....1..0..0..0..0
%e A250731 ..0..1..0..0..1....0..1..0..0..1....0..0..0..0..0....0..1..0..0..1
%e A250731 ..1..0..1..0..1....1..0..1..1..1....1..0..0..1..0....1..0..1..0..1
%Y A250731 Row 2 of A250729.
%K A250731 nonn
%O A250731 1,1
%A A250731 _R. H. Hardin_, Nov 27 2014