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A200777 T(n,k)=Number of nXk 0..2 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

%I A200777 #7 Jul 22 2025 15:56:05
%S A200777 3,3,3,2,5,2,7,5,5,7,9,20,13,20,9,6,37,31,31,37,6,22,31,77,342,77,31,
%T A200777 22,30,144,217,1368,1368,217,144,30,20,273,553,1806,7725,1806,553,273,
%U A200777 20,75,218,1438,18801,13422,13422,18801,1438,218,75,105,1054,3849,66784,194535
%N A200777 T(n,k)=Number of nXk 0..2 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.
%C A200777 Table starts
%C A200777 ..3....3....2......7........9.........6..........22...........30............20
%C A200777 ..3....5....5.....20.......37........31.........144..........273...........218
%C A200777 ..2....5...13.....31.......77.......217.........553.........1438..........3849
%C A200777 ..7...20...31....342.....1368......1806.......18801........66784.........80772
%C A200777 ..9...37...77...1368.....7725.....13422......194535.......980702.......1678693
%C A200777 ..6...31..217...1806....13422.....91755......633413......4472626......30905995
%C A200777 .22..144..553..18801...194535....633413....17965438....171117355.....537341613
%C A200777 .30..273.1438..66784...980702...4472626...171117355...2189118202....9237040535
%C A200777 .20..218.3849..80772..1678693..30905995...537341613...9237040535..159001066390
%C A200777 .75.1054.9634.855668.24878620.209517906.14614583388.342978784324.2722231659577
%H A200777 R. H. Hardin, <a href="/A200777/b200777.txt">Table of n, a(n) for n = 1..178</a>
%e A200777 Some solutions for n=6 k=4
%e A200777 ..0..0..0..0....0..0..1..1....0..0..0..0....0..0..0..0....0..0..0..0
%e A200777 ..0..1..2..1....0..0..1..2....0..1..2..1....0..0..2..2....0..0..2..1
%e A200777 ..0..2..1..2....0..0..1..2....0..1..2..1....0..0..1..1....0..1..2..1
%e A200777 ..0..1..1..2....0..1..1..2....0..1..2..1....1..1..1..2....0..1..2..2
%e A200777 ..0..1..2..2....0..2..1..2....0..2..2..2....1..1..2..2....1..1..2..2
%e A200777 ..1..1..2..2....1..2..2..2....1..1..2..2....1..2..2..2....1..1..2..2
%Y A200777 Column 1 includes A003409((n+1)/3) and A000984(n/3)
%K A200777 nonn,tabl
%O A200777 1,1
%A A200777 _R. H. Hardin_ Nov 22 2011