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%I #4 Feb 04 2014 06:18:14
%S 81,402,402,2061,2700,2061,10488,18062,18062,10488,53401,122882,
%T 167387,122882,53401,271420,836966,1580672,1580672,836966,271420,
%U 1382012,5677464,15073049,21527380,15073049,5677464,1382012,7030000,38493628
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays colored with the maximum plus the minimum minus the lower median of every 2X2 subblock
%C Table starts
%C ........81.........402..........2061..........10488..........53401
%C .......402........2700.........18062.........122882.........836966
%C ......2061.......18062........167387........1580672.......15073049
%C .....10488......122882.......1580672.......21527380......297032042
%C .....53401......836966......15073049......297032042.....6020147131
%C ....271420.....5677464.....142485336.....4061242860...119868748036
%C ...1382012....38493628....1348599340....55269492484..2375043608680
%C ...7030000...261361496...12751872544...754851641410.47198092150236
%C ..35777132..1774467580..120966824930.10327406038280
%C .182015816.12042475374.1143637823692
%H R. H. Hardin, <a href="/A237182/b237182.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 16]
%F k=2: [order 40]
%e Some solutions for n=3 k=4
%e ..0..2..0..0..1....0..0..1..0..1....0..0..2..2..1....0..2..0..0..2
%e ..0..1..1..2..1....0..0..2..2..0....0..0..0..2..1....0..2..2..1..1
%e ..1..2..2..2..1....0..2..1..1..2....2..1..1..0..1....2..2..2..2..1
%e ..2..1..0..0..1....2..2..1..1..1....2..2..1..0..2....1..1..0..2..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 04 2014