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%I #9 Oct 03 2025 08:25:28
%S 1,12,78,546,3914,28554,211242,1577878,11867186,89815404,682642050,
%T 5211283212,39897460856,306446600454,2358644800468,18199380449274,
%U 140644480480176,1089068472750998,8443172123261506,65564035662489652
%N Number of -6..6 arrays x(0..n-1) of n elements with zero sum and elements alternately strictly increasing and strictly decreasing.
%C Column 6 of A200057
%H R. H. Hardin, <a href="/A200055/b200055.txt">Table of n, a(n) for n = 1..200</a>
%e Some solutions for n=6
%e .-2....0...-3...-1...-3....5...-2....5....2....1...-3....0....4...-6...-1...-5
%e ..4....5...-5...-2....1...-3....5...-5....1....0....0...-1...-3....3....0....1
%e .-5...-3....4....1...-6....1...-6....2....5....1...-1....1....1...-4...-2...-6
%e ..4...-2....2...-3....6...-1....5...-2...-6...-3....2...-2...-6....3....5....3
%e .-5...-4....5....6....0....1...-4....1....1....4...-3....3....6....1...-2....1
%e ..4....4...-3...-1....2...-3....2...-1...-3...-3....5...-1...-2....3....0....6
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 13 2011