A250792 - OEIS

%I #7 Nov 20 2018 09:08:42

%S 54,162,482,1430,4258,12706,37986,113694,340562,1020650,3059890,

%T 9175558,27518466,82538994,247584194,742687022,2227929970,6683527738,

%U 20050058898,60149128086,180445287074,541331666882,1623986612002,4871943058750

%N 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 R. H. Hardin, <a href="/A250792/b250792.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 10*a(n-2) + 11*a(n-4) - 6*a(n-5).

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

%F 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 a(n) = -3 - (-1)^n/4 + 2^(1+n) + (23*3^(1+n))/4 + n.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 3 of A250797.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2014