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A250792 Number of (n+1) X (3+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.

%I A250792 #7 Nov 20 2018 09:08:42
%S A250792 54,162,482,1430,4258,12706,37986,113694,340562,1020650,3059890,
%T A250792 9175558,27518466,82538994,247584194,742687022,2227929970,6683527738,
%U A250792 20050058898,60149128086,180445287074,541331666882,1623986612002,4871943058750
%N A250792 Number of (n+1) X (3+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 A250792 R. H. Hardin, <a href="/A250792/b250792.txt">Table of n, a(n) for n = 1..210</a>
%F A250792 Empirical: a(n) = 6*a(n-1) - 10*a(n-2) + 11*a(n-4) - 6*a(n-5).
%F A250792 Conjectures from _Colin Barker_, Nov 20 2018: (Start)
%F A250792 G.f.: 2*x*(27 - 81*x + 25*x^2 + 79*x^3 - 48*x^4) / ((1 - x)^2*(1 + x)*(1 - 2*x)*(1 - 3*x)).
%F A250792 a(n) = -3 - (-1)^n/4 + 2^(1+n) + (23*3^(1+n))/4 + n.
%F A250792 (End)
%e A250792 Some solutions for n=4:
%e A250792 ..0..0..1..0....0..0..1..0....1..0..1..0....0..1..0..1....0..0..1..0
%e A250792 ..0..1..0..1....0..0..0..1....1..0..1..0....0..0..1..0....0..0..0..1
%e A250792 ..0..1..0..1....0..0..0..1....0..1..0..1....0..0..0..1....0..0..1..0
%e A250792 ..0..0..1..0....0..0..1..0....0..0..1..0....1..1..1..0....0..0..1..0
%e A250792 ..0..1..0..1....0..0..1..1....0..0..1..1....1..1..1..1....0..0..1..1
%Y A250792 Column 3 of A250797.
%K A250792 nonn
%O A250792 1,1
%A A250792 _R. H. Hardin_, Nov 27 2014