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%I #7 Nov 20 2018 03:34:15
%S 144,396,990,2426,5688,12950,28692,62274,132890,279864,583196,1205236,
%T 2474328,5053216,10277030,20831790,42114880,84962234,171112172,
%U 344149014,691415474,1387878796,2783929300,5581085336,11183577088,22401796180
%N Number of (5+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="/A250787/b250787.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 5*a(n-3) + 13*a(n-4) - 16*a(n-5) + 2*a(n-6) + 5*a(n-7) - 2*a(n-8).
%F Empirical g.f.: 2*x*(72 - 234*x + 171*x^2 + 259*x^3 - 420*x^4 + 70*x^5 + 148*x^6 - 64*x^7) / ((1 - x)^4*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - _Colin Barker_, Nov 20 2018
%e Some solutions for n=4:
%e ..0..1..0..0..0....0..0..0..0..1....0..0..0..0..1....0..0..0..1..0
%e ..0..1..0..0..1....0..0..0..1..0....0..0..0..0..1....1..1..1..0..1
%e ..0..1..0..0..1....0..0..0..1..0....0..0..0..0..1....1..1..1..1..0
%e ..0..1..0..1..0....0..0..0..1..0....1..1..1..1..0....1..1..1..1..1
%e ..0..1..0..1..0....0..0..0..1..1....1..1..1..1..0....1..1..1..1..1
%e ..1..0..1..0..1....0..0..0..1..1....1..1..1..1..1....1..1..1..1..1
%Y Row 5 of A250783.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 27 2014
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