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%I #6 Jun 18 2022 18:00:45
%S 81,211,211,537,669,537,1523,2111,2111,1523,4309,7995,7900,7995,4309,
%T 12723,29673,40199,40199,29673,12723,37701,117703,189527,316921,
%U 189527,117703,37701,113771,462885,1031110,2265637,2265637,1031110,462885
%N T(n,k) = Number of (n+1) X (k+1) 0..2 arrays with the maximum plus the upper median plus the lower median of every 2 X 2 subblock equal.
%C Table starts
%C ......81......211.......537.........1523..........4309...........12723
%C .....211......669......2111.........7995.........29673..........117703
%C .....537.....2111......7900........40199........189527.........1031110
%C ....1523.....7995.....40199.......316921.......2265637........19772641
%C ....4309....29673....189527......2265637......23065072.......308682677
%C ...12723...117703...1031110.....19772641.....308682677......6486271600
%C ...37701...462885...5389465....163853211....3749944595....120596994045
%C ..113771..1868937..30143115...1470283561...50416764317...2482328271821
%C ..344885..7534429.165929972..12922658673..649519074615..48561262896722
%C .1055235.30744153.944003155.117130624281.8682755057576.984788620200753
%H R. H. Hardin, <a href="/A236884/b236884.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 16]
%F k=2: [order 31]
%F k=3: [order 63]
%e Some solutions for n=3, k=4
%e ..2..2..2..2..1....0..2..1..2..1....2..2..2..2..2....2..2..0..2..1
%e ..2..2..2..2..2....2..1..2..0..2....2..2..2..0..2....0..2..2..2..2
%e ..2..2..1..2..1....2..1..2..1..2....2..2..2..2..2....2..2..2..2..0
%e ..1..2..2..2..2....2..1..2..1..2....1..2..0..2..1....1..2..1..2..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 01 2014
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