%I #8 Nov 20 2018 07:30:30

%S 24,66,180,490,1336,3646,9956,27194,74288,202950,554460,1514802,

%T 4138504,11306590,30890164,84393482,230567264,629921462,1720977420,

%U 4701797730,12845550264,35094695950,95880492388,261950376634,715661738000

%N Number of (n+1) X (2+1) 0..1 arrays with nondecreasing min(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="/A250791/b250791.txt">Table of n, a(n) for n = 1..210</a>

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

%F Conjectures from _Colin Barker_, Nov 20 2018: (Start)

%F G.f.: 2*x*(12 - 15*x - 6*x^2 + 8*x^3) / ((1 - x)^2*(1 - 2*x - 2*x^2)).

%F a(n) = (-6 + (39-23*sqrt(3))*(1-sqrt(3))^n + 39*(1+sqrt(3))^n + 23*sqrt(3)*(1+sqrt(3))^n + 6*n) / 9.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 2 of A250797.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2014