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%I #8 May 17 2018 09:11:58
%S 2,36,142,376,778,1404,2294,3504,5074,7060,9502,12456,15962,20076,
%T 24838,30304,36514,43524,51374,60120,69802,80476,92182,104976,118898,
%U 134004,150334,167944,186874,207180,228902,252096,276802,303076,330958,360504
%N Number of -n..n arrays x(0..2) of 3 elements with zeroth through 2nd differences all nonzero.
%C Row 3 of A199943.
%H R. H. Hardin, <a href="/A199944/b199944.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5).
%F Conjectures from _Colin Barker_, May 17 2018: (Start)
%F G.f.: 2*x*(1 + 15*x + 19*x^2 + 13*x^3) / ((1 - x)^4*(1 + x)).
%F a(n) = 6*n - 10*n^2 + 8*n^3 for n even.
%F a(n) = -2 + 6*n - 10*n^2 + 8*n^3 for n odd.
%F (End)
%e Some solutions for n=6:
%e ..5....2...-6...-6....1....5...-1....2....6....2...-3...-6...-4....1....5...-3
%e .-4....1...-3....3...-6....6...-2...-5...-2....4....3....2....1....4....3...-5
%e .-2...-1....6...-5....1....1....4....2....3....1...-5...-1...-5....6....6....3
%Y Cf. A199943.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 12 2011
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