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%I #5 Mar 31 2012 12:36:21
%S 1,1,3,1,5,9,1,7,23,23,1,9,43,83,57,1,11,69,181,299,141,1,13,101,317,
%T 827,1081,351,1,15,139,491,1741,3773,3931,875,1,17,183,703,3141,9385,
%U 17197,14293,2181,1,19,233,953,5127,19301,50035,78407,51955,5435,1,21,289,1241
%N T(n,k)=Number of arrays of -k..k integers x(1..n) with every x(i) being in a subsequence of length 1, 2 or 3 with sum zero
%C Table starts
%C ....1......1.......1.......1........1........1.........1.........1.........1
%C ....3......5.......7.......9.......11.......13........15........17........19
%C ....9.....23......43......69......101......139.......183.......233.......289
%C ...23.....83.....181.....317......491......703.......953......1241......1567
%C ...57....299.....827....1741.....3141.....5127......7799.....11257.....15601
%C ..141...1081....3773....9385....19301....35121.....58661.....91953....137245
%C ..351...3931...17197...50035...115761...231121....416291....694877...1093915
%C ..875..14293...78407..268453...706591..1571745...3109443...5641657...9576643
%C .2181..51955..357403.1438203..4292223.10581553..22837977..44687885..81096625
%C .5435.188859.1629369.7705011.26065517.71181241.167468295.352989885.683733847
%H R. H. Hardin, <a href="/A193702/b193702.txt">Table of n, a(n) for n = 1..1738</a>
%e Some solutions for n=7 k=6
%e .-2...-5...-3...-4...-1...-1...-4...-3...-3...-3...-5...-2...-2...-4...-5...-3
%e ..0....5....3....4....3....1....4...-1....4...-1....1....4....0....6....5....3
%e ..2...-5....1...-2...-2....0....5....4...-1....4....4...-2....2...-2....0....6
%e ..1....2....2....2...-6...-1...-6....0....1...-3...-3...-2...-5....2...-5...-6
%e .-3...-2...-3...-2....6...-5....1...-1...-2....2...-2...-2....5...-4....5....3
%e ..5....6....0....2...-6....6....3....4....1...-6....5....4....3....4...-2...-5
%e .-5...-4....0...-2....0...-6...-3...-3....0....4...-3....0...-3...-4...-3....2
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_ Aug 02 2011