A229105 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.

4, 16, 16, 64, 256, 64, 256, 4096, 4096, 256, 1024, 63248, 257984, 63248, 1024, 4096, 974864, 14747432, 14747432, 974864, 4096, 16384, 14988504, 818683176, 2868497664, 818683176, 14988504, 16384, 65536, 230263568, 44773333904

Offset

1,1

Comments

Table starts

......4..........16...............64.................256..................1024

.....16.........256.............4096...............63248................974864

.....64........4096...........257984............14747432.............818683176

....256.......63248.........14747432..........2868497664..........531085813392

...1024......974864........818683176........531085813392.......322730734532144

...4096....14988504......44773333904......96355251717448....191717335254838000

..16384...230263568....2433605818736...17357082345304488.113048691194875930568

..65536..3535340280..131915396019176.3117995723618536688

.262144.54259841344.7141796191458336

Links

R. H. Hardin, Table of n, a(n) for n = 1..71

Formula

Empirical for column k:

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

k=2: [order 23 linear recurrence].

Example

Some solutions for n=4 k=4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..1..1....0..0..1..2....0..0..1..0....0..0..1..0
..0..1..3..0....0..1..1..1....0..1..2..1....0..0..2..1....0..1..2..0
..1..1..3..2....3..2..0..0....2..2..0..0....1..2..0..0....0..2..2..2

Crossrefs

Column 1 is A000302.

Sequence in context: A232431 A267974 A267997 * A223585 A202680 A263568

Adjacent sequences: A229102 A229103 A229104 * A229106 A229107 A229108

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 13 2013

Status

approved