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T(n,k)=Number of (n+3)X(k+3) binary arrays with consecutive windows of four bits considered as a binary number nondecreasing in every row and column
8

%I #5 Mar 31 2012 12:36:53

%S 65536,83521,83521,104976,113856,104976,130321,153874,153874,130321,

%T 160000,206145,225858,206145,160000,194481,273683,330853,330853,

%U 273683,194481,234256,359970,481798,533832,481798,359970,234256,279841,468980

%N T(n,k)=Number of (n+3)X(k+3) binary arrays with consecutive windows of four bits considered as a binary number nondecreasing in every row and column

%C Table starts

%C ..65536..83521..104976..130321...160000...194481....234256....279841....331776

%C ..83521.113856..153874..206145...273683...359970....468980....605203....773669

%C .104976.153874..225858..330853...481798...695114....991196...1394929...1936228

%C .130321.206145..330853..533832...857408..1360328...2121734...3245653...4866027

%C .160000.273683..481798..857408..1515902..2631416...4457228...7350643..11802908

%C .194481.359970..695114.1360328..2631416..4958318...9044252..15949741..27226555

%C .234256.468980..991196.2121734..4457228..9044252..17632598..33032581..59606286

%C .279841.605203.1394929.3245653..7350643.15949741..33032581..65399112.124211368

%C .331776.773669.1936228.4866027.11802908.27226555..59606286.124211368.247473102

%C .390625.979972.2650602.7152307.18474721.45087162.103928266.227205936.473559376

%H R. H. Hardin, <a href="/A202939/b202939.txt">Table of n, a(n) for n = 1..7806</a>

%F Empirical: column k is a polynomial in n of degree k+3

%e Some solutions for n=2 k=3

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

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

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

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

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

%Y Column 1 is A000583(n+15)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Dec 26 2011