%I #5 Feb 02 2014 07:58:20
%S 256,704,704,1936,1632,1936,5984,3928,3928,5984,18496,10776,8416,
%T 10776,18496,61472,30248,20776,20776,30248,61472,204304,92328,53200,
%U 46416,53200,92328,204304,712352,286168,149608,108824,108824,149608,286168
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the sum of all four elements of every 2X2 subblock equal
%C Table starts
%C .....256......704.....1936.....5984....18496....61472...204304...712352
%C .....704.....1632.....3928....10776....30248....92328...286168...938568
%C ....1936.....3928.....8416....20776....53200...149608...431584..1327432
%C ....5984....10776....20776....46416...108824...282048...755752..2169408
%C ...18496....30248....53200...108824...235456...566936..1419088..3823352
%C ...61472....92328...149608...282048...566936..1274544..2995048..7603440
%C ..204304...286168...431584...755752..1419088..2995048..6637792.15955528
%C ..712352...938568..1327432..2169408..3823352..7603440.15955528
%C .2483776..3112424..4162576..6387224.10606336.19947032
%C .8957984.10749192.13679848.19785696.31051928
%H R. H. Hardin, <a href="/A237015/b237015.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k (apparently all rows and columns satisfy the same order 15 linear recurrence):
%F k=1..6: [same linear recurrence of order 15]
%e Some solutions for n=4 k=4
%e ..0..1..1..1..2....1..2..2..0..1....2..0..3..0..2....1..1..2..2..2
%e ..2..0..1..0..0....1..1..0..3..1....3..1..2..1..3....3..1..2..0..2
%e ..0..1..1..1..2....1..2..2..0..1....0..2..1..2..0....0..2..1..3..1
%e ..2..0..1..0..0....2..0..1..2..2....2..2..1..2..2....2..2..1..1..1
%e ..1..0..2..0..3....0..3..1..1..0....2..0..3..0..2....1..1..2..2..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 02 2014