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A250784 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.

%I A250784 #8 Nov 19 2018 12:58:41
%S A250784 18,46,106,238,518,1106,2326,4838,9978,20446,41686,84658,171398,
%T A250784 346166,697786,1404398,2823078,5669266,11375926,22812358,45722618,
%U A250784 91603646,183463606,367341938,735354918,1471795606,2945348026,5893538638
%N A250784 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 A250784 R. H. Hardin, <a href="/A250784/b250784.txt">Table of n, a(n) for n = 1..210</a>
%F A250784 Empirical: a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).
%F A250784 Conjectures from _Colin Barker_, Nov 19 2018: (Start)
%F A250784 G.f.: 2*x*(9 - 13*x - 3*x^2 + 8*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)).
%F A250784 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 A250784 (End)
%e A250784 Some solutions for n=4:
%e A250784 ..0..0..1..0..0....0..1..0..0..0....1..1..1..0..1....0..1..0..1..1
%e A250784 ..0..0..1..0..1....1..0..1..1..1....1..1..1..1..0....0..1..0..1..1
%e A250784 ..0..0..1..1..0....1..0..1..1..1....1..1..1..1..1....0..1..0..1..1
%Y A250784 Row 2 of A250783.
%K A250784 nonn
%O A250784 1,1
%A A250784 _R. H. Hardin_, Nov 27 2014