A229105 - OEIS

%I #8 Sep 13 2013 19:59:47

%S 4,16,16,64,256,64,256,4096,4096,256,1024,63248,257984,63248,1024,

%T 4096,974864,14747432,14747432,974864,4096,16384,14988504,818683176,

%U 2868497664,818683176,14988504,16384,65536,230263568,44773333904

%N T(n,k) = number of nXk 0..3 arrays of the median of the corresponding element, the element to the east and the element to the south in a larger (n+1)X(k+1) 0..3 array.

%C Table starts

%C ......4..........16...............64.................256..................1024

%C .....16.........256.............4096...............63248................974864

%C .....64........4096...........257984............14747432.............818683176

%C ....256.......63248.........14747432..........2868497664..........531085813392

%C ...1024......974864........818683176........531085813392.......322730734532144

%C ...4096....14988504......44773333904......96355251717448....191717335254838000

%C ..16384...230263568....2433605818736...17357082345304488.113048691194875930568

%C ..65536..3535340280..131915396019176.3117995723618536688

%C .262144.54259841344.7141796191458336

%H R. H. Hardin, <a href="/A229105/b229105.txt">Table of n, a(n) for n = 1..71</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-1).

%F k=2: [order 23 linear recurrence].

%e Some solutions for n=4 k=4

%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0

%e ..0..0..0..0....0..0..1..1....0..0..1..2....0..0..1..0....0..0..1..0

%e ..0..1..3..0....0..1..1..1....0..1..2..1....0..0..2..1....0..1..2..0

%e ..1..1..3..2....3..2..0..0....2..2..0..0....1..2..0..0....0..2..2..2

%Y Column 1 is A000302.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Sep 13 2013