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Number of (2+1) X (n+1) 0..2 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.
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%I #8 Nov 23 2018 06:06:12

%S 125,431,1325,3867,11029,31215,88421,251819,722525,2089551,6088189,

%T 17854683,52646213,155906639,463263029,1380089259,4119295693,

%U 12312797679,36841923341,110320248347,330524536565,990650861871,2970006427525

%N Number of (2+1) X (n+1) 0..2 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 R. H. Hardin, <a href="/A250900/b250900.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 40*a(n-2) + 82*a(n-3) - 91*a(n-4) + 52*a(n-5) - 12*a(n-6).

%F Conjectures from _Colin Barker_, Nov 23 2018: (Start)

%F G.f.: x*(125 - 819*x + 2015*x^2 - 2393*x^3 + 1392*x^4 - 324*x^5) / ((1 - x)^3*(1 - 2*x)^2*(1 - 3*x)).

%F a(n) = 23/2 - 2^(4+n) + (7*3^(2+n))/2 + 2*n + 3*2^(3+n)*n + n^2.

%F (End)

%e Some solutions for n=4:

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

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

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

%Y Row 2 of A250898.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014