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%I #8 May 17 2018 10:59:46
%S 6,68,288,840,1948,3914,7074,11862,18732,28244,40970,57598,78816,
%T 105444,138284,178282,226362,283598,351026,429852,521230,626492,
%U 746910,883944,1038982,1213616,1409348,1627896,1870884,2140158,2437454,2764750,3123900
%N Number of -n..n arrays x(0..4) of 5 elements with zero sum and elements alternately strictly increasing and strictly decreasing.
%C Row 5 of A200057.
%H R. H. Hardin, <a href="/A200059/b200059.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) -a(n-3) -2*a(n-5) +2*a(n-6) +a(n-8) -2*a(n-10) +a(n-11).
%F Empirical g.f.: 2*x*(3 + 28*x + 76*x^2 + 135*x^3 + 168*x^4 + 159*x^5 + 105*x^6 + 51*x^7 + 10*x^8 + x^9) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - _Colin Barker_, May 17 2018
%e Some solutions for n=6:
%e ..1...-1....3...-6...-4...-1....1....4....6...-3....5...-1....1....1....1...-2
%e ..0....2...-6....2....3...-5....2...-6...-1...-5...-6....2...-1....5...-2....6
%e ..1...-2....4...-3...-3....5...-6....3....3....5....6...-4....4...-2....2...-5
%e .-3....5...-5....4....4...-1....4...-3...-5....1...-4....2...-3...-1...-5....1
%e ..1...-4....4....3....0....2...-1....2...-3....2...-1....1...-1...-3....4....0
%Y Cf. A200057.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 13 2011
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