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T(n,k)=Number of nXk 0..2 arrays with no element equal to the average of its horizontal and vertical neighbors
9

%I #5 Mar 31 2012 12:36:29

%S 3,6,6,10,34,10,28,246,246,28,66,1736,5032,1736,66,164,12450,98356,

%T 98356,12450,164,400,89528,1933358,5184780,1933358,89528,400,982,

%U 644328,37989740,279785830,279785830,37989740,644328,982,2406,4638654,746250884

%N T(n,k)=Number of nXk 0..2 arrays with no element equal to the average of its horizontal and vertical neighbors

%C Table starts

%C ....3.........6............10.................28.....................66

%C ....6........34...........246...............1736..................12450

%C ...10.......246..........5032..............98356................1933358

%C ...28......1736.........98356............5184780..............279785830

%C ...66.....12450.......1933358..........279785830............41434710920

%C ..164.....89528......37989740........15068331840..........6117749044788

%C ..400....644328.....746250884.......811669674888........903529041581340

%C ..982...4638654...14659367358.....43723066740718.....133441483281347232

%C .2406..33398106..287967404918...2355282493094894...19707781710109683796

%C .5898.240473126.5656823960766.126874994917842426.2910613305873428168598

%H R. H. Hardin, <a href="/A197442/b197442.txt">Table of n, a(n) for n = 1..112</a>

%e Some solutions for n=6 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Oct 15 2011