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%I #5 Mar 31 2012 12:35:55
%S 1,1,1,1,2,1,1,2,2,2,1,3,5,5,2,1,4,8,11,8,2,1,4,12,23,21,10,3,1,5,15,
%T 36,48,36,15,3,1,5,20,56,89,97,60,21,3,1,6,24,83,157,211,186,95,26,4,
%U 1,7,31,110,262,421,457,332,143,35,4,1,7,38,152,408,777,1030,938,571,212,44,4,1
%N T(n,k)=Number of nondecreasing arrangements of n numbers in -k..k with sum zero and sum of squares less than n*k*(k+1)/3
%C k*(k+1)/3 is the average squared value over -k..k
%C Table starts
%C .1..1...1...1....1.....1.....1.....1......1......1......1.......1.......1
%C .1..2...2...3....4.....4.....5.....5......6......7......7.......8.......8
%C .1..2...5...8...12....15....20....24.....31.....38.....45......53......58
%C .2..5..11..23...36....56....83...110....152....203....257.....328.....403
%C .2..8..21..48...89...157...262...408....610....877...1217....1653....2199
%C .2.10..36..97..211...421...777..1324...2155...3365...5048....7347...10411
%C .3.15..60.186..457..1030..2117..3931...6955..11808..18890...29443...44730
%C .3.21..95.332..938..2349..5278.10781..20679..37693..65031..108168..174209
%C .3.26.143.571.1828..5033.12353.27652..57369.112098.207557..367766..627381
%C .4.35.212.976.3390.10278.27893.66846.149679.315288.619458.1167215.2117218
%H R. H. Hardin, <a href="/A183935/b183935.txt">Table of n, a(n) for n = 1..642</a>
%e Some solutions for n=5
%e .-3...-2...-2...-3...-1...-3...-3...-4...-2...-4...-4...-2...-4...-3...-2...-1
%e .-2...-1...-2...-1...-1...-1...-3....0...-1...-2....0...-1....1...-1...-1...-1
%e .-1....1....0...-1...-1....0....2....1...-1....2....0...-1....1....0....0....0
%e ..3....1....2....1...-1....0....2....1....0....2....0....1....1....1....1....0
%e ..3....1....2....4....4....4....2....2....4....2....4....3....1....3....2....2
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_ Jan 08 2011
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