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%I #4 Feb 02 2014 07:07:22
%S 256,888,888,3000,3852,3000,11388,16212,16212,11388,43096,85064,78976,
%T 85064,43096,171036,429108,556322,556322,429108,171036,680872,2380742,
%U 3448154,6304776,3448154,2380742,680872,2770540,12891190,26255552
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the maximum plus the upper median plus the lower median of every 2X2 subblock equal
%C Table starts
%C ......256........888........3000..........11388............43096
%C ......888.......3852.......16212..........85064...........429108
%C .....3000......16212.......78976.........556322..........3448154
%C ....11388......85064......556322........6304776.........59328026
%C ....43096.....429108.....3448154.......59328026........759273578
%C ...171036....2380742....26255552......750471960......15309352326
%C ...680872...12891190...180781130.....8305755418.....246840494018
%C ..2770540...73033832..1407433782...107840744274....5107452443634
%C .11314280..407662600.10159143566..1291740741806...92601167163795
%C .46745212.2333365070.79598995100.16958036927472.1917855806319638
%H R. H. Hardin, <a href="/A236987/b236987.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 37]
%F k=2: [order 92]
%e Some solutions for n=3 k=4
%e ..0..2..2..2..2....0..3..1..3..2....0..2..2..0..3....0..2..0..1..1
%e ..2..3..2..3..2....3..2..3..2..3....2..3..2..3..1....3..0..3..1..3
%e ..1..2..1..2..2....3..2..3..2..3....2..2..2..1..3....1..1..1..1..0
%e ..2..3..2..3..1....0..3..0..3..2....2..3..2..3..1....3..1..3..1..3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 02 2014