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%I #7 Sep 04 2022 08:27:34
%S 1,1,1,1,3,3,1,3,5,1,1,5,15,15,5,1,5,21,29,21,9,1,7,27,75,55,37,5,1,7,
%T 47,115,111,167,39,3,1,9,57,217,479,527,295,65,5,1,9,67,297,837,1341,
%U 1275,647,107,3,1,11,97,479,1333,3067,4285,3643,1427,183,5,1,11,111,609,1989
%N T(n,k) = Number of zero-sum -k..k arrays of n elements with first through fourth differences also in -k..k.
%C Table starts
%C .1...1....1.....1......1......1.......1.......1........1........1.........1
%C .1...3....3.....5......5......7.......7.......9........9.......11........11
%C .3...5...15....21.....27.....47......57......67.......97......111.......125
%C .1..15...29....75....115....217.....297.....479......609......887......1091
%C .5..21...55...111....479....837....1333....1989.....2827.....5737......7743
%C .9..37..167...527...1341...3067....6019...11353....19601....32099.....50621
%C .5..39..295..1275...4285..11591...27087...57287...111197...203089....349901
%C .3..65..647..3643..14655..46521..126147..302317...656023..1320573...2491653
%C .5.107.1427.10245..50273.189527..592487.1606929..3900645..8671331..17926489
%C .3.183.3399.30215.176501.794867.2795067.8694999.23480657.57552991.130573921
%H R. H. Hardin, <a href="/A201439/b201439.txt">Table of n, a(n) for n = 1..447</a>
%e Some solutions for n=10, k=3
%e ..2...-2....0...-3....0....3....2....2....2....0...-1...-1....3....0....1...-1
%e ..2...-1....0....0....1....1....1....2....1...-1....1...-1....3....1...-1...-1
%e ..2...-1....1....1....1....0....1....2....1...-1....1...-1....2....2...-2....1
%e ..2...-1....1....0....1....0....2....1....1...-1....1...-1....0....3...-2....2
%e ..1....0....1...-1....1....0....2....0....1....0....0...-1...-1....2...-1....2
%e ..0....1....0...-1....0...-1....1...-1....0....0...-1....0...-2...-1....1....1
%e .-2....1...-1...-1....0...-2...-1...-1...-1....0...-1....1...-2...-3....2....0
%e .-3....0...-2....0....0...-2...-2...-1...-2....1...-1....1...-2...-3....1...-1
%e .-3....0...-1....2...-1...-1...-3...-1...-2....1....0....1...-1...-1....0...-2
%e .-1....3....1....3...-3....2...-3...-3...-1....1....1....2....0....0....1...-1
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Dec 01 2011