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%I #8 Nov 23 2018 03:17:54
%S 1229,3867,12387,39003,119359,357335,1052787,3069907,8903447,25780959,
%T 74735755,217269563,634036815,1857880039,5466025571,16140988131,
%U 47817974983,142048148015,422912961915,1261379418571,3767513043071
%N Number of (n+1) X (4+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="/A250894/b250894.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 23 2018: (Start)
%F G.f.: x*(1229 - 10881*x + 39723*x^2 - 76719*x^3 + 81484*x^4 - 42988*x^5 + 4192*x^6 + 6688*x^7 - 2560*x^8) / ((1 - x)^3*(1 - 2*x)^3*(1 - 3*x)).
%F a(n) = -265 - 21*2^n + 9604*3^(-3+n) + (226-9*2^(3+n))*n + 6*(7+9*2^n)*n^2 for n>2.
%F (End)
%e Some solutions for n=4:
%e ..1..0..1..0..1....1..1..0..0..0....2..1..1..1..0....1..2..1..0..0
%e ..1..1..2..1..2....2..2..1..1..2....2..1..1..1..1....1..2..1..0..0
%e ..1..1..2..1..2....1..1..0..0..1....2..1..1..1..1....1..2..2..1..2
%e ..0..0..1..0..1....1..1..0..0..2....2..1..1..2..2....0..1..1..0..1
%e ..0..0..1..0..2....1..1..0..0..2....2..1..1..2..2....0..2..2..1..2
%Y Column 4 of A250898.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 28 2014
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