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%I #11 Mar 19 2018 22:09:19
%S 37,125,413,1333,4213,13111,40357,123271,374509,1133503,3421621,
%T 10309399,31021885,93262255,280198405,841455367,2526160141,7582215967,
%U 22754413909,68279363575,204871514077,614683748239,1844194375333,5532878824423
%N Number of (n+1) X (1+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.
%C Column 1 of A250898.
%H R. H. Hardin, <a href="/A250891/b250891.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-1) - 23*a(n-2) + 28*a(n-3) - 12*a(n-4) for n > 6.
%F Empirical g.f.: x*(37 - 171*x + 264*x^2 - 132*x^3 - 8*x^4 + 2*x^5) / ((1 - x)*(1 - 2*x)^2*(1 - 3*x)). - _Colin Barker_, Mar 19 2018
%e Some solutions for n=4:
%e 2 1 1 0 1 0 1 1 1 1 1 1 2 1 1 1 1 1 1 1
%e 2 2 2 1 2 1 1 1 1 1 0 0 2 1 0 0 1 1 1 1
%e 2 2 2 1 1 0 0 0 1 1 1 1 1 2 0 0 0 0 0 0
%e 0 0 1 0 1 0 2 2 1 1 0 0 1 2 2 2 1 1 2 2
%e 1 1 2 2 2 2 0 0 0 0 0 1 0 1 1 1 1 1 2 2
%Y Cf. A250898.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 28 2014
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