%I #6 Apr 28 2021 12:40:40
%S 81,398,398,1940,2262,1940,9608,12276,12276,9608,47952,68906,68892,
%T 68906,47952,237952,391672,380270,380270,391672,237952,1181504,
%U 2259386,2285619,2393308,2285619,2259386,1181504,5866176,12874198,13917166,15926522
%N T(n,k) = Number of (n+1) X (k+1) 0..2 arrays colored with the maximum plus the lower median of every 2 X 2 subblock.
%C Table starts
%C ........81........398........1940.........9608.........47952.........237952
%C .......398.......2262.......12276........68906........391672........2259386
%C ......1940......12276.......68892.......380270.......2285619.......13917166
%C ......9608......68906......380270......2393308......15926522......110056116
%C .....47952.....391672.....2285619.....15926522.....123925495.....1040732508
%C ....237952....2259386....13917166....110056116....1040732508....11313665204
%C ...1181504...12874198....83440732....727209392....8210225326...107996912362
%C ...5866176...73197080...483431170...4738099148...61055186760...964588443772
%C ..29136768..418190364..2925674836..32015122020..491935338326..9640207475306
%C .144679680.2392155730.17483477028.217298090312.4018284920822.99641407754442
%H R. H. Hardin, <a href="/A236719/b236719.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 16].
%F k=2: [order 36] for n > 38.
%e Some solutions for n=3, k=4
%e ..0..2..2..0..1....0..1..2..2..0....0..0..1..2..2....0..1..2..2..2
%e ..0..0..1..0..0....0..0..0..1..0....2..1..0..1..2....1..1..0..0..2
%e ..1..1..1..2..1....2..1..1..1..2....0..1..1..0..0....0..2..0..0..1
%e ..1..0..2..2..1....2..1..0..2..2....0..0..2..0..0....2..2..1..1..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 30 2014