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A250846 Number of (n+1) X (1+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction. 1

%I

%S 100,543,2670,12311,54410,233683,983950,4085631,16796370,68555723,

%T 278351030,1125823351,4540620730,18274604163,73435058910,294750719471,

%U 1182035443490,4737241699003,18976271027590,75987005717991

%N Number of (n+1) X (1+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

%C Column 1 of A250853.

%H R. H. Hardin, <a href="/A250846/b250846.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) -35*a(n-2) +50*a(n-3) -24*a(n-4); a(n) = (832*4^n-846*3^n+204*2^n+2)/12.

%F G.f.: x*(100 - 457*x + 740*x^2 - 384*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)) (conjectured). - _Colin Barker_, Jan 18 2018

%e Some solutions for n=4

%e ..3..2....2..0....3..0....0..0....1..1....1..1....3..3....3..2....3..0....3..3

%e ..0..0....0..2....0..0....0..0....0..0....0..0....1..1....0..0....0..1....3..3

%e ..2..3....0..2....2..2....2..3....3..3....1..1....2..3....0..1....1..2....1..1

%e ..2..3....0..3....1..1....1..2....0..0....2..3....2..3....0..1....0..1....1..1

%e ..1..2....0..3....0..1....0..2....1..3....0..2....0..1....0..2....1..3....1..1

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014

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Last modified September 26 05:00 EDT 2020. Contains 337346 sequences. (Running on oeis4.)