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%I #4 Jan 31 2014 06:47:49
%S 81,303,303,1162,1791,1162,4627,10702,10702,4627,18527,66853,98380,
%T 66853,18527,75330,419301,956456,956456,419301,75330,307321,2680296,
%U 9360398,14757359,9360398,2680296,307321,1264403,17221539,93804194,230126265
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the maximum plus the lower median minus the minimum of every 2X2 subblock equal
%C Table starts
%C .......81........303..........1162............4627.............18527
%C ......303.......1791.........10702...........66853............419301
%C .....1162......10702.........98380..........956456...........9360398
%C .....4627......66853........956456........14757359.........230126265
%C ....18527.....419301.......9360398.......230126265........5737086630
%C ....75330....2680296......93804194......3697318630......148094642882
%C ...307321...17221539.....947327860.....60011383119.....3864575378035
%C ..1264403..111813697....9682975968....987175371637...102225528160171
%C ..5216986..729282012...99543701888..16341810901082..2719153814334744
%C .21640527.4786748055.1030061727604.272220635630305.72722922283523296
%H R. H. Hardin, <a href="/A236819/b236819.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 15]
%F k=2: [order 34]
%F k=3: [order 87]
%e Some solutions for n=3 k=4
%e ..0..0..0..0..0....0..0..2..0..2....0..0..0..0..0....0..0..0..2..0
%e ..0..2..2..1..2....2..0..0..0..0....1..2..0..2..0....0..2..0..0..2
%e ..0..1..1..2..1....0..0..2..2..2....0..0..0..2..0....1..0..2..0..2
%e ..0..2..2..1..1....2..0..2..2..2....2..2..0..1..0....0..2..0..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 31 2014
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