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%I #5 Mar 31 2012 12:36:44
%S 4,6,6,4,2,4,1,21,21,1,4,9,52,9,4,6,56,29,29,56,6,4,13,246,112,246,13,
%T 4,1,110,701,261,261,701,110,1,4,32,844,846,4544,846,844,32,4,6,198,
%U 426,1720,22324,22324,1720,426,198,6,4,41,2478,4193,45532,16334,45532,4193
%N T(n,k)=Number of nXk 0..3 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
%C Table starts
%C .4...6....4.....1.......4.......6........4........1..........4..........6
%C .6...2...21.....9......56......13......110.......32........198.........41
%C .4..21...52....29.....246.....701......844......426.......2478.......5990
%C .1...9...29...112.....261.....846.....1720.....4193.......8065......16693
%C .4..56..246...261....4544...22324....45532....32314.....313710....1126721
%C .6..13..701...846...22324...16334...363693...211755....3708666....1743841
%C .4.110..844..1720...45532..363693..1129682..1136762...16354832...80822317
%C .1..32..426..4193...32314..211755..1136762..5464208...23238776...89540916
%C .4.198.2478..8065..313710.3708666.16354832.23238776..458459214.3056235023
%C .6..41.5990.16693.1126721.1743841.80822317.89540916.3056235023.2605975384
%H R. H. Hardin, <a href="/A201451/b201451.txt">Table of n, a(n) for n = 1..312</a>
%F T(n,1) = binomial(4,n modulo 4). For a 0..z array, T(n,1) = binomial(z+1, n modulo (z+1)).
%e Some solutions for n=10 k=3
%e ..0..0..0....0..0..0....0..0..1....0..0..1....0..0..0....0..1..1....0..0..1
%e ..0..1..1....0..0..1....0..0..2....0..0..1....0..0..0....0..1..1....0..0..2
%e ..0..1..2....0..1..1....0..0..2....0..0..2....0..1..1....0..1..1....0..1..2
%e ..0..1..2....0..1..1....0..1..2....0..1..2....1..1..2....0..1..2....0..1..2
%e ..0..1..2....1..1..2....1..1..3....0..1..2....1..2..3....0..2..2....0..1..3
%e ..1..1..3....2..2..2....1..1..3....1..2..2....1..2..3....0..2..2....1..2..3
%e ..1..2..3....2..2..3....1..1..3....1..3..3....1..2..3....0..3..3....1..2..3
%e ..2..2..3....2..2..3....2..2..3....1..3..3....1..2..3....2..3..3....1..2..3
%e ..2..2..3....3..3..3....2..2..3....2..3..3....2..3..3....2..3..3....1..3..3
%e ..3..3..3....3..3..3....2..3..3....2..3..3....2..3..3....2..3..3....2..3..3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Dec 01 2011