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%I #8 May 17 2018 11:00:03
%S 2,28,84,218,444,808,1330,2068,2996,4230,5740,7552,9746,12348,15304,
%T 18782,22732,27144,32162,37784,43912,50790,58332,66496,75494,85280,
%U 95736,107166,119452,132524,146646,161752,177688,194822,213008,232132,252534
%N Number of -n..n arrays x(0..3) of 4 elements with sum zero and with zeroth through 3rd differences all nonzero.
%C Row 4 of A200038.
%H R. H. Hardin, <a href="/A200040/b200040.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = a(n-2) +2*a(n-3) -a(n-5) -a(n-6) -a(n-7) -a(n-8) +2*a(n-10) +a(n-11) -a(n-13).
%F Empirical g.f.: 2*x*(1 + 14*x + 41*x^2 + 93*x^3 + 152*x^4 + 212*x^5 + 240*x^6 + 243*x^7 + 191*x^8 + 138*x^9 + 79*x^10 + 36*x^11) / ((1 - x)^4*(1 + x)*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, May 17 2018
%e Some solutions for n=6:
%e ..2...-2...-1....6...-2....5....4...-5...-1...-6...-2....1...-4...-3...-6...-1
%e ..5...-3....2...-3....6...-6...-5....3....3....6...-3...-4....1...-1...-1....6
%e .-2....6....1...-5....2...-5...-1...-2...-3...-2....3....6....2....5....5...-2
%e .-5...-1...-2....2...-6....6....2....4....1....2....2...-3....1...-1....2...-3
%Y Cf. A200038.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 12 2011
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