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%I #7 Nov 22 2018 16:33:35
%S 127,431,1450,4750,15111,47061,144442,439056,1326285,3990883,11981256,
%T 35923998,107646283,322490625,966132822,2894737036,8674725225,
%U 26000484927,77943849220,233694315930,700761297831,2101539929629
%N Number of (n+1) X (2+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="/A250892/b250892.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 12*a(n-1) - 60*a(n-2) + 162*a(n-3) - 255*a(n-4) + 234*a(n-5) - 116*a(n-6) + 24*a(n-7) for n>9.
%F Conjectures from _Colin Barker_, Nov 22 2018: (Start)
%F G.f.: x*(127 - 1093*x + 3898*x^2 - 7364*x^3 + 7674*x^4 - 3984*x^5 + 498*x^6 + 328*x^7 - 88*x^8) / ((1 - x)^3*(1 - 2*x)^3*(1 - 3*x)).
%F a(n) = (567 - 3807*2^n + 7225*3^n - 54*(-1+15*2^n)*n + 54*(-2+3*2^n)*n^2) / 108 for n>2.
%F (End)
%e Some solutions for n=4:
%e ..1..1..0....2..0..0....2..1..0....1..0..0....1..0..0....2..2..0....1..1..1
%e ..1..1..1....2..0..0....2..1..2....2..2..2....1..1..1....1..1..1....2..2..2
%e ..1..1..1....1..1..1....2..1..2....2..2..2....0..0..0....0..0..0....0..0..0
%e ..1..2..2....2..2..2....1..0..1....2..2..2....0..0..2....0..1..1....0..2..2
%e ..0..1..1....2..2..2....0..1..2....1..1..1....0..0..2....0..1..2....0..2..2
%Y Column 2 of A250898.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 28 2014
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