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%I #4 Jan 30 2014 06:12:26
%S 81,442,442,2464,3492,2464,13720,27406,27406,13720,76404,216340,
%T 313360,216340,76404,424600,1707838,3607280,3607280,1707838,424600,
%U 2361716,13499232,42032622,62377580,42032622,13499232,2361716,13136192,106577620
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays colored with the maximum plus the upper median minus the lower median of every 2X2 subblock
%C Table starts
%C ........81.........442..........2464...........13720...........76404
%C .......442........3492.........27406..........216340.........1707838
%C ......2464.......27406........313360.........3607280........42032622
%C .....13720......216340.......3607280........62377580......1099360056
%C .....76404.....1707838......42032622......1099360056.....29705776060
%C ....424600....13499232.....489450096.....19356846358....800348545256
%C ...2361716...106577620....5684197999....338611786558..21427121287833
%C ..13136192...841345444...65906387212...5938320805688.575347045288652
%C ..73071732..6643410412..766873371754.104483857316574
%C .406402784.52475002544.8913443952908
%H R. H. Hardin, <a href="/A236710/b236710.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 19]
%F k=2: [order 59] for n>60
%e Some solutions for n=2 k=4
%e ..0..2..0..0..1....1..1..0..0..2....0..0..1..0..2....0..0..2..2..0
%e ..1..0..0..0..2....0..0..0..2..0....0..0..2..1..0....1..1..0..2..1
%e ..1..1..2..0..2....1..0..0..2..1....0..1..1..2..1....0..1..2..1..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 30 2014