A228986 T(n,k) = number of nXk 0..1 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..1 array.

2, 4, 4, 8, 16, 8, 16, 64, 64, 16, 32, 252, 512, 252, 32, 64, 992, 3928, 3928, 992, 64, 128, 3900, 29808, 56472, 29808, 3900, 128, 256, 15328, 224720, 796568, 796568, 224720, 15328, 256, 512, 60228, 1690048, 11130176, 20729216, 11130176, 1690048, 60228

Offset

1,1

Comments

Table starts

...2......4........8..........16............32...............64

...4.....16.......64.........252...........992.............3900

...8.....64......512........3928.........29808...........224720

..16....252.....3928.......56472........796568.........11130176

..32....992....29808......796568......20729216........533254872

..64...3900...224720....11130176.....533254872......25205141664

.128..15328..1690048...155031688...13667372880....1186378174632

.256..60228.12696384..2156604552..349809115952...55757344229608

.512.236624.95336800.29985039328.8948779914072.2619135139987152

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 6*a(n-1) -7*a(n-2) -6*a(n-3) +6*a(n-4)

k=3: [order 11]

k=4: [order 35] for n>36

Example

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

Crossrefs

Column 1 is A000079.

Sequence in context: A283857 A227442 A282316 * A188910 A189111 A181217

Adjacent sequences: A228983 A228984 A228985 * A228987 A228988 A228989

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 10 2013

Status

approved