A299740 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 220, 128, 16, 32, 512, 1578, 1578, 512, 32, 64, 2048, 11303, 21111, 11303, 2048, 64, 128, 8192, 81105, 280642, 280642, 81105, 8192, 128, 256, 32768, 582032, 3742524, 6896530, 3742524, 582032, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

...1.....2.......4.........8...........16.............32...............64

...2.....8......32.......128..........512...........2048.............8192

...4....32.....220......1578........11303..........81105...........582032

...8...128....1578.....21111.......280642........3742524.........49914496

..16...512...11303....280642......6896530......170243005.......4203272237

..32..2048...81105...3742524....170243005.....7790212998.....356575568843

..64..8192..582032..49914496...4203272237...356575568843...30260326859957

.128.32768.4177161.665759775.103785926879.16322570202905.2568233775595684

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) = 4*a(n-1)

k=3: [order 8]

k=4: [order 24]

k=5: [order 79]

Example

Some solutions for n=5 k=4
..0..0..0..1. .0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..0
..0..0..0..1. .0..0..0..1. .1..1..1..0. .0..0..0..1. .0..0..0..0
..0..0..0..1. .1..1..1..0. .0..0..0..1. .1..1..0..0. .0..0..0..0
..1..1..1..0. .0..0..0..0. .0..0..0..1. .1..0..1..0. .1..1..1..1
..1..1..1..0. .1..0..0..1. .0..0..0..1. .1..1..0..1. .0..1..1..1

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A305523 A298970 A316960 * A316815 A299661 A320371

Adjacent sequences: A299737 A299738 A299739 * A299741 A299742 A299743

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 18 2018

Status

approved