%I #8 Nov 23 2018 05:31:02

%S 10875,31215,91030,265546,764315,2168405,6060594,16732140,45832201,

%T 125162059,342287192,940831202,2606118783,7287014385,20581424254,

%U 58711891192,169046356181,490755132023,1434774937860,4219275237870

%N Number of (n+1) X (6+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="/A250896/b250896.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 12*a(n-1) - 60*a(n-2) + 162*a(n-3) - 255*a(n-4) + 234*a(n-5) - 116*a(n-6) + 24*a(n-7) for n>9.

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

%F G.f.: x*(10875 - 99285*x + 368950*x^2 - 715664*x^3 + 755858*x^4 - 402400*x^5 + 50022*x^6 + 63432*x^7 - 26568*x^8) / ((1 - x)^3*(1 - 2*x)^3*(1 - 3*x)).

%F a(n) = (-8787 + 3389*2^n + 169*3^(3+n) + (14186-99*2^(4+n))*n + 36*(145+33*2^(1+n))*n^2) / 4 for n>2.

%F (End)

%e Some solutions for n=3:

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

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

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

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

%Y Column 6 of A250898.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014