%I #4 Feb 11 2014 12:22:10
%S 256,1120,1120,5038,6964,5038,23838,44648,44648,23838,115028,305054,
%T 408824,305054,115028,567446,2123660,4021892,4021892,2123660,567446,
%U 2840760,15253914,40288632,57342898,40288632,15253914,2840760,14437142
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the maximum plus the upper median plus the minimum minus the lower median of every 2X2 subblock equal
%C Table starts
%C .......256........1120..........5038..........23838..........115028
%C ......1120........6964.........44648.........305054.........2123660
%C ......5038.......44648........408824........4021892........40288632
%C .....23838......305054.......4021892.......57342898.......832743124
%C ....115028.....2123660......40288632......832743124.....17532208572
%C ....567446....15253914.....418287818....12585917094....385376900438
%C ...2840760...111492872....4418514021...194171070966...8672245375519
%C ..14437142...834134686...47970957966..3092262164912.202110825015400
%C ..74266834..6338273516..529234228994.50231979219254
%C .386657722.49073750056.5972920589738
%H R. H. Hardin, <a href="/A237694/b237694.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 34]
%e Some solutions for n=2 k=4
%e ..0..2..1..3..3....0..2..2..1..3....0..3..2..2..3....0..2..2..1..2
%e ..3..1..2..0..2....1..3..1..2..0....2..1..0..0..1....1..3..1..2..1
%e ..2..2..1..3..1....0..0..2..3..1....0..3..2..2..3....2..0..2..3..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 11 2014