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%I #8 May 17 2018 11:07:03
%S 10,178,1098,4172,11962,28554,59910,114232,202314,337902,538054,
%T 823496,1218978,1753638,2461350,3381092,4557298,6040218,7886274,
%U 10158420,12926498,16267598,20266414,25015604,30616142,37177686,44818926,53667948
%N Number of -n..n arrays x(0..5) of 6 elements with zero sum and elements alternately strictly increasing and strictly decreasing.
%C Row 6 of A200057.
%H R. H. Hardin, <a href="/A200060/b200060.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +2*a(n-5) -a(n-6) -a(n-7) +2*a(n-8) -a(n-10) -2*a(n-11) +3*a(n-12) -a(n-13).
%F Empirical g.f.: 2*x*(5 + 74*x + 292*x^2 + 622*x^3 + 910*x^4 + 1045*x^5 + 999*x^6 + 782*x^7 + 452*x^8 + 162*x^9 + 24*x^10 + x^11) / ((1 - x)^6*(1 + x)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, May 17 2018
%e Some solutions for n=6:
%e ..3...-3...-2....4....4...-2...-5....0....1....1....2....1....1...-2...-3...-1
%e ..5...-2...-3....3....5...-6....3....2...-6...-2....5...-6...-2....3....2....6
%e .-5...-4....3....5...-4....6....2...-3....0....5...-1....1....6...-2....1...-3
%e .-3....3...-5...-6...-2....0....5....4...-4...-6....2...-2...-6....2....3....0
%e .-6....1....5...-2...-5....6...-3...-6....6....6...-5....6....1...-3...-6...-2
%e ..6....5....2...-4....2...-4...-2....3....3...-4...-3....0....0....2....3....0
%Y Cf. A200057.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 13 2011