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%I #5 Mar 31 2012 12:35:55
%S 1,1,1,1,2,2,1,3,4,2,1,3,5,6,2,1,4,8,12,9,3,1,4,12,23,22,13,3,1,5,17,
%T 37,48,39,17,3,1,5,22,58,93,102,63,24,4,1,6,25,83,163,220,186,104,31,
%U 4,1,7,31,112,262,434,476,332,155,38,4,1,7,38,154,414,794,1061,979,596,226,49
%N T(n,k)=Number of nondecreasing arrangements of n numbers in -k..k with sum zero and sum of squares not greater 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...3...3....4.....4.....5.....5......6......7......7.......8.......8
%C .2..4...5...8...12....17....22....25.....31.....38.....45......53......62
%C .2..6..12..23...37....58....83...112....154....203....259.....329.....403
%C .2..9..22..48...93...163...262...414....618....877...1227....1661....2199
%C .3.13..39.102..220...434...794..1346...2190...3398...5106....7411...10494
%C .3.17..63.186..476..1061..2117..3998...7036..11808..19093...29687...44730
%C .3.24.104.332..979..2414..5278.10966..20984..37693..65732..109170..174209
%C .4.31.155.596.1888..5166.12584.28096..58118.113204.209399..370563..631264
%C .4.38.226.976.3493.10526.27893.67867.151415.315288.624895.1175933.2117218
%H R. H. Hardin, <a href="/A183927/b183927.txt">Table of n, a(n) for n = 1..642</a>
%e Some solutions for n=5 k=4
%e .-2...-3...-3...-3...-2...-2...-1...-4...-4...-2...-2...-2...-2...-2...-2...-1
%e .-2...-2...-2....0...-2...-2...-1....0...-1...-1...-2...-1...-1...-2...-2...-1
%e ..0....1....0....1...-1...-2...-1....0....1...-1....0...-1...-1....1...-2....0
%e ..2....1....1....1....2....3...-1....1....2....2....0....1....0....1....2....0
%e ..2....3....4....1....3....3....4....3....2....2....4....3....4....2....4....2
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_ Jan 08 2011
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