%I #8 Nov 19 2018 12:58:41

%S 18,46,106,238,518,1106,2326,4838,9978,20446,41686,84658,171398,

%T 346166,697786,1404398,2823078,5669266,11375926,22812358,45722618,

%U 91603646,183463606,367341938,735354918,1471795606,2945348026,5893538638

%N 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 absolute value of x(i,j)-x(i-1,j) in the j direction.

%H R. H. Hardin, <a href="/A250784/b250784.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).

%F Conjectures from _Colin Barker_, Nov 19 2018: (Start)

%F G.f.: 2*x*(9 - 13*x - 3*x^2 + 8*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)).

%F a(n) = 2^(1-n) * (2^n*(1+11*2^n) + 2*(1-sqrt(5))^n*(-2+sqrt(5)) - 2*(1+sqrt(5))^n*(2+sqrt(5))).

%F (End)

%e Some solutions for n=4:

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

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

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

%Y Row 2 of A250783.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2014