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A250778 Number of (n+1) X (3+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 A250778 #8 Nov 19 2018 09:13:59
%S A250778 46,106,230,482,990,2010,4054,8146,16334,32714,65478,131010,262078,
%T A250778 524218,1048502,2097074,4194222,8388522,16777126,33554338,67108766,
%U A250778 134217626,268435350,536870802,1073741710,2147483530,4294967174
%N A250778 Number of (n+1) X (3+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 A250778 R. H. Hardin, <a href="/A250778/b250778.txt">Table of n, a(n) for n = 1..210</a>
%F A250778 Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
%F A250778 Conjectures from _Colin Barker_, Nov 19 2018: (Start)
%F A250778 G.f.: 2*x*(23 - 39*x + 18*x^2) / ((1 - x)^2*(1 - 2*x)).
%F A250778 a(n) = 2^(5+n) - 4*n - 14.
%F A250778 (End)
%e A250778 Some solutions for n=4:
%e A250778 ..0..1..0..1....1..0..0..0....0..0..1..0....0..0..0..0....1..0..0..1
%e A250778 ..0..1..0..1....1..0..0..0....0..1..0..1....0..0..0..1....1..0..0..1
%e A250778 ..1..0..1..0....1..0..0..0....0..1..0..1....0..0..1..0....1..0..1..0
%e A250778 ..0..1..0..1....1..0..0..1....0..1..0..1....0..0..1..0....1..0..1..0
%e A250778 ..1..0..1..0....1..0..0..1....0..1..0..1....0..0..1..0....1..1..0..1
%Y A250778 Column 3 of A250783.
%K A250778 nonn
%O A250778 1,1
%A A250778 _R. H. Hardin_, Nov 27 2014