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%I #4 Jan 12 2014 07:13:24
%S 16,50,50,144,250,144,398,1120,1120,398,1076,4670,8046,4670,1076,2866,
%T 18606,53728,53728,18606,2866,7560,71710,336836,599834,336836,71710,
%U 7560,19798,270016,2000524,6353336,6353336,2000524,270016,19798,51580,998834
%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 rowwise and columnwise
%C Table starts
%C .....16.......50........144..........398............1076.............2866
%C .....50......250.......1120.........4670...........18606............71710
%C ....144.....1120.......8046........53728..........336836..........2000524
%C ....398.....4670......53728.......599834.........6353336.........63238254
%C ...1076....18606.....336836......6353336.......118826310.......2119256572
%C ...2866....71710....2000524.....63238254......2119256572......70251672970
%C ...7560...270016...11372978....592286060.....35394045432....2203799654900
%C ..19798...998834...62383454...5248500942....551086363442...64128617114034
%C ..51580..3646406..332455972..44325853698...8029786206898.1724826332820910
%C .133850.13176346.1730326282.359137867202.110154213330742
%H R. H. Hardin, <a href="/A235573/b235573.txt">Table of n, a(n) for n = 1..112</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 12]
%F k=3: [order 39]
%e Some solutions for n=3 k=4
%e ..0..1..0..0..1....1..1..1..0..1....1..1..0..0..1....0..0..0..1..1
%e ..1..1..1..0..1....1..1..1..1..1....1..1..1..0..1....0..0..1..1..0
%e ..0..1..0..1..1....1..1..0..1..0....1..0..0..1..0....0..0..0..1..1
%e ..0..0..1..1..1....1..1..0..1..0....0..1..0..0..1....1..1..1..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 12 2014