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%I #5 Mar 31 2012 12:36:37
%S 1,1,2,1,4,4,1,6,10,4,1,8,22,26,6,1,10,36,78,68,10,1,12,56,172,288,
%T 178,14,1,14,78,324,840,1098,472,22,1,16,106,546,1948,4172,4224,1276,
%U 34,1,18,136,850,3914,11962,20978,16432,3462,52,1,20,172,1252,7074,28554,74338
%N T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum and elements alternately strictly increasing and strictly decreasing
%C Table starts
%C ..1....1......1.......1........1........1.........1..........1..........1
%C ..2....4......6.......8.......10.......12........14.........16.........18
%C ..4...10.....22......36.......56.......78.......106........136........172
%C ..4...26.....78.....172......324......546.......850.......1252.......1764
%C ..6...68....288.....840.....1948.....3914......7074......11862......18732
%C .10..178...1098....4172....11962....28554.....59910.....114232.....202314
%C .14..472...4224...20978....74338...211242....514168....1115572....2215290
%C .22.1276..16432..106674...466548..1577878...4453946...10995240...24477966
%C .34.3462..64310..545698..2947742.11867186..38855488..109147062..272432422
%C .52.9496.253692.2811236.18746754.89815404.341052122.1090022120.3050199016
%H R. H. Hardin, <a href="/A200057/b200057.txt">Table of n, a(n) for n = 1..871</a>
%e Some solutions for n=7 k=6
%e ..3....0...-2....1....0...-3....0....0...-3....0...-3...-3....3...-3....0...-6
%e .-1...-3...-6....0...-1....6....2....5...-6....5...-6....0...-3...-2...-4....3
%e ..0....5....6....3....6...-3...-2...-5....4...-5....3...-1....3...-3....4...-2
%e .-4....2...-5...-4...-3...-2....1....6...-5....6...-3....4...-5....1...-6....5
%e ..4....4....1...-1...-1...-4...-5...-3....5...-3....6...-1....4...-1....6....1
%e .-3...-6....0...-3...-6....6....4....1...-1....2...-3....3...-3....6...-5....3
%e ..1...-2....6....4....5....0....0...-4....6...-5....6...-2....1....2....5...-4
%Y Column 1 is twice A077419 for n>1
%Y Row 3 is twice A171769
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_ Nov 13 2011
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