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%I #4 Jan 17 2014 15:06:09
%S 16,50,50,144,228,144,398,928,928,398,1076,3574,5196,3574,1076,2866,
%T 13346,27296,27296,13346,2866,7560,48848,137988,195428,137988,48848,
%U 7560,19798,176420,681546,1340034,1340034,681546,176420,19798,51580,631130
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the difference of the upper and lower median value of each 2X2 subblock in lexicographically nondecreasing order columnwise and nonincreasing rowwise
%C Table starts
%C .....16......50.......144.........398.........1076...........2866
%C .....50.....228.......928........3574........13346..........48848
%C ....144.....928......5196.......27296.......137988.........681546
%C ....398....3574.....27296......195428......1340034........8974124
%C ...1076...13346....137988.....1340034.....12412248......112308598
%C ...2866...48848....681546.....8974124....112308598.....1374773712
%C ...7560..176420...3311312....59037352....997114552....16500794898
%C ..19798..631130..15908352...383935642...8749889970...195824119834
%C ..51580.2242678..75789960..2474858156..76070757246..2302059880080
%C .133850.7930164.358924192.15855538026.657191443192.26894984140858
%H R. H. Hardin, <a href="/A235962/b235962.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -a(n-2) -10*a(n-3) +8*a(n-4)
%F k=2: [order 8]
%F k=3: [order 17]
%F k=4: [order 32]
%F k=5: [order 67]
%e Some solutions for n=4 k=4
%e ..1..0..0..0..0....0..1..1..1..0....0..0..0..0..0....0..1..1..0..1
%e ..0..0..0..1..1....0..0..1..1..0....0..0..0..1..1....0..0..1..1..0
%e ..0..0..1..1..1....0..1..1..1..0....0..0..0..0..0....0..1..1..1..1
%e ..1..0..0..1..1....1..1..1..1..1....0..0..1..0..1....0..0..1..1..1
%e ..0..0..0..0..1....0..1..0..1..0....1..0..0..0..0....1..0..0..1..1
%Y Column 1 is A235566
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 17 2014
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