%I #8 Nov 23 2018 06:06:03

%S 37,127,403,1229,3673,10875,32095,94729,280069,829943,2465227,7338309,

%T 21883825,65356531,195414199,584800769,1751256541,5246953839,

%U 15726181411,47147086909,141374151817,423979849067,1271637557263,3814275137529

%N 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 R. H. Hardin, <a href="/A250899/b250899.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) - 31*a(n-2) + 51*a(n-3) - 40*a(n-4) + 12*a(n-5).

%F Conjectures from _Colin Barker_, Nov 23 2018: (Start)

%F 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 a(n) = (7 - 2^(4+n) + 3^(3+n) + (2+2^(3+n))*n) / 2.

%F (End)

%e Some solutions for n=4:

%e ..1..1..1..0..0....0..2..2..1..0....2..1..1..2..1....2..2..1..2..0

%e ..2..2..2..1..1....0..2..2..1..2....2..1..1..2..1....2..2..1..2..1

%Y Row 1 of A250898.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014