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%I A250899 #8 Nov 23 2018 06:06:03
%S A250899 37,127,403,1229,3673,10875,32095,94729,280069,829943,2465227,7338309,
%T A250899 21883825,65356531,195414199,584800769,1751256541,5246953839,
%U A250899 15726181411,47147086909,141374151817,423979849067,1271637557263,3814275137529
%N A250899 Number of (1+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
%H A250899 R. H. Hardin, <a href="/A250899/b250899.txt">Table of n, a(n) for n = 1..210</a>
%F A250899 Empirical: a(n) = 9*a(n-1) - 31*a(n-2) + 51*a(n-3) - 40*a(n-4) + 12*a(n-5).
%F A250899 Conjectures from _Colin Barker_, Nov 23 2018: (Start)
%F A250899 G.f.: x*(37 - 206*x + 407*x^2 - 348*x^3 + 108*x^4) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)).
%F A250899 a(n) = (7 - 2^(4+n) + 3^(3+n) + (2+2^(3+n))*n) / 2.
%F A250899 (End)
%e A250899 Some solutions for n=4:
%e A250899 ..1..1..1..0..0....0..2..2..1..0....2..1..1..2..1....2..2..1..2..0
%e A250899 ..2..2..2..1..1....0..2..2..1..2....2..1..1..2..1....2..2..1..2..1
%Y A250899 Row 1 of A250898.
%K A250899 nonn
%O A250899 1,1
%A A250899 _R. H. Hardin_, Nov 28 2014

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