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%I #7 Nov 20 2018 03:38:17
%S 288,796,2010,5028,12036,27986,63184,139436,301786,643164,1353544,
%T 2820050,5828064,11966884,24444622,49725780,100817008,203857762,
%U 411330612,828530748,1666582118,3348596476,6722194620,13484879538
%N Number of (6+1) X (n+1) 0..1 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="/A250788/b250788.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 7*a(n-1) - 18*a(n-2) + 17*a(n-3) + 8*a(n-4) - 29*a(n-5) + 18*a(n-6) + 3*a(n-7) - 7*a(n-8) + 2*a(n-9).
%F Empirical g.f.: 2*x*(144 - 610*x + 811*x^2 + 195*x^3 - 1408*x^4 + 1026*x^5 + 137*x^6 - 421*x^7 + 128*x^8) / ((1 - x)^5*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - _Colin Barker_, Nov 20 2018
%e Some solutions for n=4:
%e ..1..0..0..0..1....1..0..0..1..0....0..0..0..0..1....0..0..1..0..1
%e ..0..1..1..1..0....1..0..0..1..0....0..0..0..0..1....1..1..0..1..0
%e ..0..1..1..1..0....1..0..0..1..0....0..0..0..1..0....1..1..0..1..0
%e ..0..1..1..1..0....1..0..0..1..0....0..0..1..0..1....1..1..0..1..0
%e ..0..1..1..1..1....1..1..1..0..1....1..1..0..1..0....1..1..0..1..0
%e ..0..1..1..1..1....1..1..1..0..1....1..1..1..0..1....1..1..1..0..1
%e ..0..1..1..1..1....1..1..1..1..0....1..1..1..0..1....1..1..1..0..1
%Y Row 6 of A250783.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 27 2014