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%I #6 Jun 22 2021 14:35:07
%S 256,1200,1200,5288,10000,5288,26320,79164,79164,26320,131280,762724,
%T 1150036,762724,131280,677344,7370124,22056220,22056220,7370124,
%U 677344,3518120,74701920,411646536,880923796,411646536,74701920,3518120
%N T(n,k) = Number of (n+1) X (k+1) 0..3 arrays with the upper median plus the lower median of every 2 X 2 subblock equal.
%C Table starts
%C ......256........1200...........5288.............26320...............131280
%C .....1200.......10000..........79164............762724..............7370124
%C .....5288.......79164........1150036..........22056220............411646536
%C ....26320......762724.......22056220.........880923796..........33233608132
%C ...131280.....7370124......411646536.......33233608132........2436563812004
%C ...677344....74701920.....8124638140.....1329345087772......191579721419964
%C ..3518120...760932408...158569999540....52079122983140....14586236067453980
%C .18477584..7859816444..3140246502408..2070941611511776..1132213042481221540
%C .97461616.81402789128.61933486884504.81772162000490880.86956201802583194276
%H R. H. Hardin, <a href="/A237007/b237007.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 15]
%F k=2: [order 42]
%e Some solutions for n=2, k=4
%e ..0..1..3..1..1....0..2..2..3..2....0..2..0..2..3....0..2..0..1..3
%e ..1..1..1..1..1....2..2..2..2..2....2..1..2..1..1....3..0..3..1..1
%e ..0..2..1..0..2....1..3..0..2..2....1..2..0..3..2....1..1..1..0..3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 02 2014