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Number of (n+1)X(1+1) 0..3 arrays with nondecreasing min(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.
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%I #8 Nov 14 2018 11:04:25

%S 120,889,5996,39187,248942,1555689,9605300,58826247,358185874,

%T 2172028005,13132419904,79233189251,477317759278,2872297644737,

%U 17270479247100,103783325757983,623401528654314,3743476771002397,22474273340351352

%N Number of (n+1)X(1+1) 0..3 arrays with nondecreasing min(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.

%H R. H. Hardin, <a href="/A250512/b250512.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 15*a(n-2) - 80*a(n-3) + 122*a(n-4) + 228*a(n-5) - 120*a(n-6) - 144*a(n-7).

%F Empirical g.f.: x*(120 - 311*x - 1094*x^2 + 2162*x^3 + 3492*x^4 - 2064*x^5 - 2304*x^6) / ((1 - x)*(1 + 2*x)*(1 - 6*x)*(1 - 2*x - 2*x^2)*(1 - 3*x - 6*x^2)). - _Colin Barker_, Nov 14 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A250519.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 24 2014