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%I #5 Mar 31 2012 12:36:42
%S 2,3,1,4,3,2,5,6,2,1,6,10,7,7,2,7,15,17,3,9,1,8,21,33,15,17,6,2,9,28,
%T 57,46,8,40,22,1,10,36,90,107,44,61,46,30,2,11,45,134,213,151,20,206,
%U 21,20,1,12,55,190,383,398,134,214,410,135,75,2,13,66,260,636,890,536,70,1055
%N T(n,k)=Number of 0..k arrays x(0..n-1) of n elements with nondecreasing average value and 0..k occur with instance counts within one of each other
%C Table starts
%C .2..3...4...5....6.....7.....8.....9...10....11.....12......13......14.......15
%C .1..3...6..10...15....21....28....36...45....55.....66......78......91......105
%C .2..2...7..17...33....57....90...134..190...260....345.....447.....567......707
%C .1..7...3..15...46...107...213...383..636...997...1492....2151....3005.....4092
%C .2..9..17...8...44...151...398...890.1774..3246...5555....9016...14012....21005
%C .1..6..40..61...20...134...536..1613.4023..8842..17681...32835...57465....95825
%C .2.22..46.206..214....70...496..2185.7215.19783..47458..102886..206061...386953
%C .1.30..21.410.1055...906...212..1882.9470.34680.104386..272088..636895..1368860
%C .2.20.135.426.3020..5719..3748...914.8404.45418.181600..591875.1665229..4181993
%C .1.75.342.228.5124.22641.31522.18675.3578.38444.232486.1015624.3582100.10821987
%H R. H. Hardin, <a href="/A200942/b200942.txt">Table of n, a(n) for n = 1..648</a>
%e Some solutions for n=8 k=8
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..2....1....2....1....1....3....3....1....2....1....1....2....1....1....1....1
%e ..1....2....1....2....8....2....2....2....4....3....7....1....2....3....2....2
%e ..4....3....4....6....3....5....6....6....3....8....3....3....8....4....5....6
%e ..7....8....3....5....6....7....4....4....5....5....8....8....4....2....3....3
%e ..5....7....8....3....5....4....7....3....6....4....5....6....6....7....7....5
%e ..8....6....5....4....4....8....8....5....7....7....4....4....5....5....4....4
%e ..6....5....6....8....7....6....5....8....8....6....6....7....7....6....8....7
%Y Column 2 is A200770
%Y Column 5 is A200895
%Y Column 6 is A200930
%Y Row 2 is A000217
%Y Row 3 is A045947 for n>1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Nov 24 2011
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