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 A250872 Number of (n+1) X (3+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction. 1

%I

%S 678,3442,16262,73122,317878,1350002,5640102,23289922,95366678,

%T 388124562,1572545542,6350471522,25583049078,102876275122,

%U 413138516582,1657456673922,6644539237078,26622304009682,106621676097222

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

%H R. H. Hardin, <a href="/A250872/b250872.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) = (1168*4^n - 1026*3^n + 216*2^n + 8)/3.

%F Empirical g.f.: 2*x*(339 - 1669*x + 2786*x^2 - 1464*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - _Colin Barker_, Nov 22 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 3 of A250877.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014

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Last modified December 1 18:36 EST 2022. Contains 358475 sequences. (Running on oeis4.)