%I #5 Mar 31 2012 12:36:43

%S 3,6,6,11,20,11,19,56,56,19,32,140,235,140,32,53,330,860,860,330,53,

%T 87,745,2910,4572,2910,745,87,142,1634,9287,22183,22183,9287,1634,142,

%U 231,3504,28452,100362,153796,100362,28452,3504,231,375,7388,84473,432048

%N T(n,k)=Number of nXk 0..2 arrays with every diagonal, row and column running average nondecreasing rightwards and downwards and diagonally

%C Table starts

%C ...3.....6.....11.......19.........32..........53............87............142

%C ...6....20.....56......140........330.........745..........1634...........3504

%C ..11....56....235......860.......2910........9287.........28452..........84473

%C ..19...140....860.....4572......22183......100362........432048........1791740

%C ..32...330...2910....22183.....153796......988216.......6002677.......34907951

%C ..53...745...9287...100362.....988216.....9005581......77316192......632331257

%C ..87..1634..28452...432048....6002677....77316192.....938925282....10844322561

%C .142..3504..84473..1791740...34907951...632331257...10844322561...177169920997

%C .231..7388.244933..7225068..196209473..4971371594..120031503310..2771232663847

%C .375.15366.697065.28510387.1073245835.37852928161.1282802588833.41769721151444

%H R. H. Hardin, <a href="/A201155/b201155.txt">Table of n, a(n) for n = 1..161</a>

%e Some solutions for n=3 k=7

%e ..0..0..0..0..0..0..1....0..0..0..0..0..0..0....0..0..0..0..1..1..1

%e ..0..1..1..1..2..1..1....0..0..1..2..2..2..2....0..0..1..1..1..2..2

%e ..1..1..1..1..2..2..2....0..0..1..1..2..1..1....1..1..2..2..2..2..2

%Y Column 1 is A001911(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Nov 27 2011