A317517 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 255, 128, 16, 32, 512, 2032, 2032, 512, 32, 64, 2048, 16193, 32256, 16193, 2048, 64, 128, 8192, 129042, 512096, 512096, 129042, 8192, 128, 256, 32768, 1028335, 8130048, 16198017, 8130048, 1028335, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

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

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

...4.....32......255........2032..........16193...........129042

...8....128.....2032.......32256.........512096..........8130048

..16....512....16193......512096.......16198017........512358002

..32...2048...129042.....8130048......512358002......32289056648

..64...8192..1028335...129072576....16206294085....2034862700902

.128..32768..8194796..2049155072...512618027974..128237436273216

.256.131072.65304285.32532368768.16214518668763.8081548422775938

Links

R. H. Hardin, Table of n, a(n) for n = 1..420

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1)

k=3: a(n) = 8*a(n-1) -a(n-2) +6*a(n-3)

k=4: a(n) = 16*a(n-1) -6*a(n-2) +64*a(n-3)

k=5: [order 8]

k=6: [order 15]

k=7: [order 34]

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A303421 A301407 A213418 * A300182 A317532 A222659

Adjacent sequences: A317514 A317515 A317516 * A317518 A317519 A317520

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 30 2018

Status

approved