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A250943 Number of (1+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. 1

%I #11 Nov 23 2018 21:18:17

%S 37,155,599,2247,8189,29281,103093,358683,1235935,4225319,14350733,

%T 48472137,162955925,545627419,1820560999,6056081319,20091759229,

%U 66499907441,219643052501,724114352379,2383286792687,7832488669255

%N Number of (1+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="/A250943/b250943.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 6*a(n-2) - 15*a(n-3) + 14*a(n-4) + 12*a(n-5).

%F Empirical g.f.: x*(37 - 67*x - 109*x^2 + 138*x^3 + 108*x^4) / ((1 - 3*x)*(1 - x - x^2)*(1 - 2*x - 4*x^2)). - _Colin Barker_, Nov 23 2018

%e Some solutions for n=4:

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

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

%Y Row 1 of A250942.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014

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