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%I #5 Mar 31 2012 12:36:45
%S 1,1,1,1,3,3,1,3,5,3,1,5,15,19,5,1,5,21,45,45,11,1,7,27,95,169,129,21,
%T 1,7,47,173,443,643,345,39,1,9,57,285,977,2191,2509,1031,73,1,9,67,
%U 431,1905,5963,11107,10129,2969,129,1,11,97,633,3373,13635,36569,57203,41031
%N T(n,k)=Number of zero-sum -k..k arrays of n elements with first and second differences also in -k..k
%C Table starts
%C ...1....1......1.......1.......1........1.........1.........1..........1
%C ...1....3......3.......5.......5........7.........7.........9..........9
%C ...3....5.....15......21......27.......47........57........67.........97
%C ...3...19.....45......95.....173......285.......431.......633........879
%C ...5...45....169.....443.....977.....1905......3373......5555.......8655
%C ..11..129....643....2191....5963....13635.....27647.....51753......90021
%C ..21..345...2509...11107...36569....99143....232969....492307.....958025
%C ..39.1031..10129...57203..229949...734607...1990383...4764587...10355033
%C ..73.2969..41031..296293.1451137..5477087..17103271..46365813..112608305
%C .129.8803.166337.1541117.9210249.40989699.147612131.453359171.1229793047
%H R. H. Hardin, <a href="/A201873/b201873.txt">Table of n, a(n) for n = 1..1912</a>
%e Some solutions for n=6 k=7
%e ..5....0...-5...-2....6...-3...-3...-6....2....3....7...-5...-1...-5....0....1
%e ..1...-4...-7...-3....0...-4...-1...-1....4...-2....3....1...-3...-5...-2...-5
%e ..3...-3...-2....1....0...-2....0...-2....2....0....2....3....1....1....0...-4
%e .-2...-3....4....2...-4....0....2....1....0....3...-2....3....5....6....1....3
%e .-4....3....5....3...-4....2....3....3...-4....0...-6...-1....2....5....1....4
%e .-3....7....5...-1....2....7...-1....5...-4...-4...-4...-1...-4...-2....0....1
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_ Dec 06 2011
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