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%I #4 Jan 31 2014 06:13:45
%S 81,255,255,825,1231,825,2817,6217,6217,2817,9717,34163,47831,34163,
%T 9717,34317,191657,420133,420133,191657,34317,122305,1116735,3722333,
%U 6154349,3722333,1116735,122305,442285,6597729,34857701,89430035,89430035
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the maximum plus the upper median plus the minimum of every 2X2 subblock equal
%C Table starts
%C ......81........255..........825...........2817..............9717
%C .....255.......1231.........6217..........34163............191657
%C .....825.......6217........47831.........420133...........3722333
%C ....2817......34163.......420133........6154349..........89430035
%C ....9717.....191657......3722333.......89430035........2074360867
%C ...34317....1116735.....34857701.....1381705469.......51617074157
%C ..122305....6597729....327044595....21112919819.....1250715634759
%C ..442285...39752795...3142571647...330530592515....31213918081267
%C .1612085..241456349..30163324455..5132785239389...766423213825979
%C .5935493.1481423855.292580627371.80558311836989.19091407245029811
%H R. H. Hardin, <a href="/A236798/b236798.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 20]
%F k=2: [order 38]
%F k=3: [order 83]
%e Some solutions for n=3 k=4
%e ..0..1..2..1..1....0..0..2..0..2....0..0..1..1..1....0..2..0..2..1
%e ..2..0..0..1..1....2..2..2..2..0....1..1..1..0..0....0..2..0..2..0
%e ..1..1..2..1..1....0..2..0..2..2....0..1..0..1..1....2..0..2..0..2
%e ..2..0..1..0..2....2..1..2..2..0....1..1..1..1..0....2..0..2..2..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 31 2014